text stringlengths 2 1.14k | label int64 0 1 |
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automorphism group; genus 2 surface; real algebraic curves fields of real algebraic functions; reduced Whitehead group; Hasse principle; norm mapping | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic plane with prescribed singularities; orientable curves | 0 |
automorphism group; genus 2 surface; real algebraic curves Teichmüller spaces; moduli spaces of real algebraic curves | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic curves; quadrature domain; Schwarzian reflection; canonical foliation | 0 |
automorphism group; genus 2 surface; real algebraic curves narrow Mordell-Weil lattice; sphere packing; algebraic equations; inverse Galois problem; group of rational points on an elliptic curve; Kodaira- Néron model; height pairing; Néron-Severi group; rational elliptic surface; Weyl groups as Galois groups | 0 |
automorphism group; genus 2 surface; real algebraic curves Cremona group; algebraic torus; del Pezzo surface; conic bundle | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic geometry; knot theory; rigid isotopy; flexible curves | 0 |
automorphism group; genus 2 surface; real algebraic curves triangular automorphism; algebraic group; automorphism group | 0 |
automorphism group; genus 2 surface; real algebraic curves codes on curves; Goppa codes; hermitean curve; generator matrix; automorphism group; stabilizer | 0 |
automorphism group; genus 2 surface; real algebraic curves order of automorphism group; K3 surface | 0 |
automorphism group; genus 2 surface; real algebraic curves immersions of the circle into surface; immersion invariants; complexification of a real curve; complex orientation of a real algebraic curve | 0 |
automorphism group; genus 2 surface; real algebraic curves Cantor's algorithm; Jacobian group; hyperelliptic curves; genus 4; binary field; projective coordinates; public key encryption | 0 |
automorphism group; genus 2 surface; real algebraic curves Brauer group of algebraic surface; Brauer group of function field; characteristic p | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic model; affine surface; rational fibration; birational diffeomorphism; affine complexification, Kodaira dimension | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic curve; Hilbert's 16th problem; smoothing of singularities; isotopy classification; real loci of non-singular algebraic curves of degeee 8 | 0 |
automorphism group; genus 2 surface; real algebraic curves plane algebraic curve; complex projective curve; genus; intersection multiplicity; Riemann surface | 0 |
automorphism group; genus 2 surface; real algebraic curves elliptic surface; rational elliptic surface; automorphism group; Mordell-Weil group; \(J\) map | 0 |
automorphism group; genus 2 surface; real algebraic curves linear groups; real curves; projective curves; function fields; strong Hasse principle; homogeneous spaces; existence of \(K\)-rational points; weak approximation; density of local points; diagonal image; central isogeny; principal homogeneous spaces; projectiv... | 0 |
automorphism group; genus 2 surface; real algebraic curves Algebraic curves; algebraic function fields; automorphism groups of curves in positive characteristic; Stöhr-Voloch theory; curves with many points over finite fields | 0 |
automorphism group; genus 2 surface; real algebraic curves Picard groups; moduli space of genus g algebraic curves; line bundles on the moduli functor; admissible coverings; divisor classes on moduli space | 0 |
automorphism group; genus 2 surface; real algebraic curves Brauer group; Picard group; algebraic surface; class group; affine algebraic variety | 0 |
automorphism group; genus 2 surface; real algebraic curves real Riemann surface; algebraic curve; topological type; algorithm | 0 |
automorphism group; genus 2 surface; real algebraic curves linear algebraic group; outer automorphism; Hermitian form; involution | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic curves; branched coverings; random maps; Bergman kernel | 0 |
automorphism group; genus 2 surface; real algebraic curves Morse function; regular homotopy; real algebraic surface; eversion of the sphere; closed halfway model; immersions; Boy surfaces | 0 |
automorphism group; genus 2 surface; real algebraic curves moduli spaces of algebraic curves; free fermions over a compact Riemann surface; soliton equations; theta functions; cobordism theory; formal groups; non-abelian conformal field theory; conformal block; gauge symmetries | 0 |
automorphism group; genus 2 surface; real algebraic curves real meromorphic functions; real algebraic curves | 0 |
automorphism group; genus 2 surface; real algebraic curves length of Lie module; automorphism group; rational Hodge structures; Mumford Tate group; Hodge Tate module; root system; cohomology spaces of projective algebraic varieties | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic variety; automorphism; minimal model; Mori cone; contraction; birational transformation; Fano variety; Cremona group; rationality; singularity | 0 |
automorphism group; genus 2 surface; real algebraic curves smooth four-manifold; moduli of differential-geometric structures; moduli of vector bundles; spin; complex algebraic surface; classification; Dirac operator; instantons; rational curves; Del Pezzo surfaces | 0 |
automorphism group; genus 2 surface; real algebraic curves moduli space of curves; tropical curves; automorphism group; symmetric complex | 0 |
automorphism group; genus 2 surface; real algebraic curves simple Harnack curves; real algebraic toric hypersurfaces | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic curves; positive characteristic; automorphism groups; many automorphisms | 0 |
automorphism group; genus 2 surface; real algebraic curves second homology group; mapping class group; orientable surface; maximal systems of isotopy classes of nonintersecting simple closed curves; bordism classes of fiber bundles; Picard group; moduli space; Francetta conjecture | 0 |
automorphism group; genus 2 surface; real algebraic curves bitangent to a quartic surface; real algebraic varieties; Euler characteristic | 0 |
automorphism group; genus 2 surface; real algebraic curves affine surface; automorphism group; group action; amalgamated product | 0 |
automorphism group; genus 2 surface; real algebraic curves endomorphism ring; real algebraic structure of complex elliptic curves as real algebraic surfaces; complex multiplication; real algebraic torus | 0 |
automorphism group; genus 2 surface; real algebraic curves monodromy; algebraic curves; mapping class group | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic cycles; Chow group; motive; finite-dimensional motive; Bloch's conjecture; generalized Hodge conjecture; Bloch-Beilinson filtration; Beauville's ``splitting property'' conjecture; hyperkähler varieties; Fano varieties of lines on cubic fourfolds; Lehn... | 0 |
automorphism group; genus 2 surface; real algebraic curves trigonal curve; real elliptic surface; \textit{dessins d'enfants}; type of real algebraic curve | 0 |
automorphism group; genus 2 surface; real algebraic curves Schur function; \(\tau-\)functions; algebraic curves of arbitrary genus; Pluecker coordinate; Riemann \(\theta-\)function; Klein \(\sigma-\)function; KP flow directions; fundamental bi-differential; Weierstrass' \(\zeta-\) and \(\rho-\)functions | 0 |
automorphism group; genus 2 surface; real algebraic curves Fermat surface; algebraic cycles; Néron-Severi group | 0 |
automorphism group; genus 2 surface; real algebraic curves \(K3\) surface; symplectic group action; period domain; period map; inverse period map; automorphic form; Siegel upper half plane of genus \(2\) | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic cycles; Beauville's ``splitting property'' conjecture; Bloch-Beilinson filtration; Bloch's conjecture; Chow group; Fano varieties of lines on cubic fourfolds; finite-dimensional motive; hyperkähler varieties; motive; non-symplectic automorphism | 0 |
automorphism group; genus 2 surface; real algebraic curves Hilbert's 16th problem; Seifert form of a link; Murasugi-Tristram inequality; quasipositive braids; topology of real plane algebraic curves; M-curves; degree; complex orientations | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic surface; diametrical surface; polar surface; asymptotic direction; invariant group; reflections | 0 |
automorphism group; genus 2 surface; real algebraic curves moduli space; stable Riemann surface; stable real algebraic curve | 0 |
automorphism group; genus 2 surface; real algebraic curves Hirzebruch surface; Galois group; gonality; automorphism; defining equation; field extension; ruled surface | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic curves; automorphism groups; finite fields | 0 |
automorphism group; genus 2 surface; real algebraic curves compact Riemann surface; automorphism group; splitting of the polarized Jacobian variety; group action | 0 |
automorphism group; genus 2 surface; real algebraic curves bivariate polynomial system; real roots isolation; plane (space) algebraic curves; topology; isotopic approximation | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic schemes; algebraic varieties; Jacobians; group schemes; Riemann-Roch theorem; dimension theory; divisors; morphisms; Chow's lemma; differential forms; completions; formal schemes; Zariski's main theorem; non-singular algebraic curves; GAGA; vanishing ... | 0 |
automorphism group; genus 2 surface; real algebraic curves Conic; parametrization of algebraic curves; group law for algebraic curves; determinatal variety | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic curves; finite fields; rational points; Stöhr-Voloch theory; automorphism groups | 0 |
automorphism group; genus 2 surface; real algebraic curves affine space; triangular automorphism; algebraic group; regular action | 0 |
automorphism group; genus 2 surface; real algebraic curves parametric system; biological network; multistationarity; block triangular; real algebraic surface; border curve | 0 |
automorphism group; genus 2 surface; real algebraic curves bivariate polynomial; plane curve; random Riemann surface; absolute factorization; algebraic geometry; continuation methods; monodromy; symmetric group; algorithms; Maple code | 0 |
automorphism group; genus 2 surface; real algebraic curves \(K3\) surface; Enriques surface; automorphism group; Petersen graph | 0 |
automorphism group; genus 2 surface; real algebraic curves complemented ideal; real analytic set; extension operator; algebraic curves | 0 |
automorphism group; genus 2 surface; real algebraic curves topology of real algebraic curves; rotation number; ovals; \(M\)-curves | 0 |
automorphism group; genus 2 surface; real algebraic curves Hilbert functions; not smoothable singular curves; algebraic curve; arithmetic genus; Castelnuovo's bound; gaps for the values of the genera of smooth curves | 0 |
automorphism group; genus 2 surface; real algebraic curves fat points; germ of a complex algebraic surface; cotangent cohomology; rational surface singularity; tangent cone; hypersurface singularity; quotient singularity; hyperplane sections; partition curves; deformation; Harrison cohomology | 0 |
automorphism group; genus 2 surface; real algebraic curves automorphism group; additive group; algebraic actions | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic surface; zero set of a holomorphic one-form; genus of an irreducible curve; Kodaira's classification of surfaces | 0 |
automorphism group; genus 2 surface; real algebraic curves orders of automorphism groups of Riemann surfaces; Kulkarni surface; number of ovals; symmetries; real forms of Accola-MacLachlan surfaces | 0 |
automorphism group; genus 2 surface; real algebraic curves Humbert configuration; curves of genus 2; real multiplication; Jacobian; Rosati involution; Humbert's criterion; explicit embedding | 0 |
automorphism group; genus 2 surface; real algebraic curves pseudoholomorphic curves; real algebraic curves; equisingular family; cubic resolvent; sextic curve in the affine plane which is not isotopic to any real algebraic sextic curve; isotopy classification of real algebraic affine \(M\)-curves of degree 6 | 0 |
automorphism group; genus 2 surface; real algebraic curves affine algebraic surface; Brauer group; class group; Picard group | 0 |
automorphism group; genus 2 surface; real algebraic curves genus three curves; algebraic correspondences; Calabi-Yau threefolds; Hodge structures; variation of Hodge structures; cycle maps | 0 |
automorphism group; genus 2 surface; real algebraic curves Parshin symbol; linear group; algebraic surface; discrete valuation field | 0 |
automorphism group; genus 2 surface; real algebraic curves fundamental group of closed oriented surface; reducible representations in the projective general linear group; Higgs bundles; real projective bundles over the surface | 0 |
automorphism group; genus 2 surface; real algebraic curves \(K3\) surface; automorphism; alternating group | 0 |
automorphism group; genus 2 surface; real algebraic curves moduli space of compact Riemann surfaces of genus \(g\); algebraic curves | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic vector bundles; real analytic geometry; algebraic group | 0 |
automorphism group; genus 2 surface; real algebraic curves genus two curves; del-Pezzo surface; symplectic invariant; enumerative invariant | 0 |
automorphism group; genus 2 surface; real algebraic curves moduli space of curves; smooth complex curves; effective \(1\)-cycles; stabilizers of curves; algebraic set; group actions; proper action; improper action; weakly proper action; orbifolds; weak orbifolds; rational homology manifold; tree-of-spheres; W-curves; m... | 0 |
automorphism group; genus 2 surface; real algebraic curves Algebraic curves; higher genus; cryptography; Elliptic curves; secret sharing schemes; authentication codes; frameproof codes; key distribution schemes; broadcast encryption; and sequences | 0 |
automorphism group; genus 2 surface; real algebraic curves topology of real algebraic curves; Viro method; patchworking; rational ruled surfaces; pseudoholomorphic curves | 0 |
automorphism group; genus 2 surface; real algebraic curves dessins d'enfant; Riemann surface; quasi-platonic surface; automorphism group; symmetries | 0 |
automorphism group; genus 2 surface; real algebraic curves homogeneous vector bundles; holomorphic functions; Lie groups; complex analysis; Lie group actions; complex spaces; Lie homomorphism; Lie algebra; automorphism group; compact homogeneous complex manifolds; flag manifolds; normalizer theorem; Tits fibration; ind... | 0 |
automorphism group; genus 2 surface; real algebraic curves theta divisor; Neron-Tate height; arbitrary genus; projective varieties; Falting's theorem; algebraic curve; rational points; Szpiro's conjecture; jacobians; elliptic curves | 0 |
automorphism group; genus 2 surface; real algebraic curves non-orientable surface; Klein surface; automorphism group; symmetric crosscap number | 0 |
automorphism group; genus 2 surface; real algebraic curves Chow group; rational surface; finite group of classes of algebraic cycles; finite field | 0 |
automorphism group; genus 2 surface; real algebraic curves Coxeter group; Beauville group; Beauville structure; Beauville surface; real surface | 0 |
automorphism group; genus 2 surface; real algebraic curves homology of algebraic curves; automorphisms; mapping class group; absolute Galois group; combinatorial group theory | 0 |
automorphism group; genus 2 surface; real algebraic curves projective algebraic curves; Hilbert functions; degree; genus; gonality; maximal rank; linear normality | 0 |
automorphism group; genus 2 surface; real algebraic curves complements of branch curves; fundamental group; moduli space of surfaces of general type; Veronese surface | 0 |
automorphism group; genus 2 surface; real algebraic curves deformation of real algebraic curves | 0 |
automorphism group; genus 2 surface; real algebraic curves rational fibration method; number of irreducible rational curves; degrees of Severi varieties; divisor classes; ruled surface; Néron-Severi group; minimal desingularization; tangential locus | 0 |
automorphism group; genus 2 surface; real algebraic curves smooth projective varieties; flag varieties; Miyaoka's semipositivity theorem; cotangent bundle; rational surfaces; divisorial contractions; fibrations; crystalline differential operators; étale fundamental group; semistability; reflexives sheaves; semipositive... | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic surfaces; algebraic curves | 0 |
automorphism group; genus 2 surface; real algebraic curves rationality of moduli space of curves of genus 2; rationality of moduli space of nodal cubics | 0 |
automorphism group; genus 2 surface; real algebraic curves characterization of finite group of polynomial automorphisms; algebraic compactification | 0 |
automorphism group; genus 2 surface; real algebraic curves real reductive group; admissible representation; multiplicity; hyperfunction; unitary representation; spherical variety; symmetric space | 0 |
automorphism group; genus 2 surface; real algebraic curves elliptic curves; cryptosystems; discrete logarithm; group of rational points; elliptic curve over a finite field; practical implementations; algorithms; running times | 0 |
automorphism group; genus 2 surface; real algebraic curves curves on cubic surface; Hilbert function; Rao module; Eckardt points | 0 |
automorphism group; genus 2 surface; real algebraic curves Kähler-Einstein metrics; first Chern class; hyperkähler varieties; Calabi-Yau varieties; holonomy; algebraic foliations; fundamental group | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic surfaces; affine-ruled surfaces; weighted projective planes; locally nilpotent derivations; additive group actions on affine \(3\)-space | 0 |
automorphism group; genus 2 surface; real algebraic curves quadratic stable range; Picard group; quadratic form; holomorphic function; Riemann surface; Bezout domain | 0 |
automorphism group; genus 2 surface; real algebraic curves Kummer surface; Jacobian of genus 2 curve; twist; Brauer-Manin obstruction | 0 |
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