text stringlengths 2 1.14k | label int64 0 1 |
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automorphism group; genus 2 surface; real algebraic curves algorithm; Newton-Puiseux expansion; roots of a polynomial; Newton polygon method; polynomial complexity; polynomial-time algorithms; formal power series; local rings of points of algebraic curves; indices of ramification; inertia; geometrical genus of a curve;... | 0 |
automorphism group; genus 2 surface; real algebraic curves invariants; binary forms; genus 3; algebraic curves | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic group; point group; completely real-closed field | 0 |
automorphism group; genus 2 surface; real algebraic curves real rational surfaces; real tubular surface; real algebraic surface | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic cone; monoid action; group action; orbit; action with unique fixed point; algebra automorphism; stable ideal; irreducible algebraic variety | 0 |
automorphism group; genus 2 surface; real algebraic curves \(G_k\)-groups; quaternion group; genus; curves; twists of curves | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic group acting effectively on symmetric space; \(L^ 2\)- cohomology; Hermitian symmetric space; Lefschetz number; fixed point | 0 |
automorphism group; genus 2 surface; real algebraic curves real K3-surface; Kähler surface; real algebraic cycles | 0 |
automorphism group; genus 2 surface; real algebraic curves Quadratic Forms; Arithmetical Symbols; Logic; Algebraic Geometry; Elliptic Curves; Algebraic Varieties; Non-standard Real numbers; Local Rings | 0 |
automorphism group; genus 2 surface; real algebraic curves differential plane curves; contact of curves; Bezout theorem; algebraic curves; elliptic curves; curvatures; Frenet frame; the group on an elliptic curve; algebraic equations | 0 |
automorphism group; genus 2 surface; real algebraic curves space curve; Picard group; curves lying on a general smooth surface; hyperplane section | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic surface; K3 surface; rational points; Zariski dense; elliptic fibrations; real topology | 0 |
automorphism group; genus 2 surface; real algebraic curves classification of real affine cubic curves; action of the group of affine isomorphisms | 0 |
automorphism group; genus 2 surface; real algebraic curves symplectic automorphism; elliptic surface; Chow group | 0 |
automorphism group; genus 2 surface; real algebraic curves level curves; algebraic surfaces; topology computation; topological properties of surfaces; surface plotting | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic model; affine surface; rational fibration; birational diffeomorphism; affine complexification | 0 |
automorphism group; genus 2 surface; real algebraic curves actions; absolute Galois group; fundamental groups of algebraic curves; Grothendieck-Teichmüller group; Galois action; uniformization; Tate elliptic curves; fundamental groups of moduli spaces | 0 |
automorphism group; genus 2 surface; real algebraic curves hyperelliptic curve; automorphism group; genus 3; dihedral invariant; moduli space | 0 |
automorphism group; genus 2 surface; real algebraic curves smooth real variety; orbifold fundamental group; \(K(\pi; \; 1)\)-complex manifolds; hyperelliptic surface; Blanchard-Calabi threefolds; moduli spaces of surfaces; Beauville surface | 0 |
automorphism group; genus 2 surface; real algebraic curves topology of real plane algebraic curves; Newton polygon; toric variety; Petrovsky inequalities; Arnol'd inequalities; real toric surfaces | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic curves; theta characteristics; convex algebraic geometry | 0 |
automorphism group; genus 2 surface; real algebraic curves automorphism groups of complex curves; classification of Riemann surfaces of genus 5; computer calculations | 0 |
automorphism group; genus 2 surface; real algebraic curves symmetric genus; Riemann surface; Riemann-Hurwitz equation; NEC group; signature | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic group; point group; completely real-closed field | 0 |
automorphism group; genus 2 surface; real algebraic curves curves of genus two; Jacobians; local fields; number fields; canonical height; height constant; Mordell-Weil group | 0 |
automorphism group; genus 2 surface; real algebraic curves automorphisms of curves; Nottingham group; cohomology of groups; Harbater-Katz-Gabber curves; algebraic covers | 0 |
automorphism group; genus 2 surface; real algebraic curves characteristic \(p\); formal schemes; Galois cover of algebraic curve; Abhyankar's conjecture; fundamental group of affine curves | 0 |
automorphism group; genus 2 surface; real algebraic curves elliptic curves; vector bundles on curves; real algebraic varieties | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic model; affine surface; rational fibration; birational diffeomorphism; affine complexification | 0 |
automorphism group; genus 2 surface; real algebraic curves elliptic surface; Hopf surface; Kodaira surface; automorphism group | 0 |
automorphism group; genus 2 surface; real algebraic curves parametric surfaces; algebraic surface; algebraic curves; geometric modelling system | 0 |
automorphism group; genus 2 surface; real algebraic curves Grothendieck group of skew-symmetric spaces; Witt group; zero-cycles; rational equivalence; real affine surface | 0 |
automorphism group; genus 2 surface; real algebraic curves Hilbert space; analytic free fields; integer spin; \(\mathbb{Z}_ n\)-asymmetric algebraic curves of genus \(g\); two-dimensional fields | 0 |
automorphism group; genus 2 surface; real algebraic curves moduli space of curves of genus g; Picard group | 0 |
automorphism group; genus 2 surface; real algebraic curves line bundle on algebraic curve; Wahl map; genus; hyperplane section of a \(K3\) surface | 0 |
automorphism group; genus 2 surface; real algebraic curves subgroup of automorphism group; characteristic p; minimal surface of general type | 0 |
automorphism group; genus 2 surface; real algebraic curves moduli space of curves; gonality; real curves; Brill-Noether theory; real algebraic curves; real Riemann surfaces | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic surfaces; orbifold fundamental group; hyperelliptic surfaces; real algebraic varieties | 0 |
automorphism group; genus 2 surface; real algebraic curves loxodromic automorphism; abelian surface; real structure | 0 |
automorphism group; genus 2 surface; real algebraic curves automorphism group; Danielewski surface; isotropy group; locally nilpotent derivation | 0 |
automorphism group; genus 2 surface; real algebraic curves symmetric space associated to the semisimple real algebraic group; torsionfree arithmetic subgroup; locally symmetric space; Hilbert modular variety; (2n)-dimensional real hyperbolic space; \(L_ 2\)-cohomology; middle intersection homology; neighborhood of a bo... | 0 |
automorphism group; genus 2 surface; real algebraic curves Riemann surface of genus 3; transformation group of order 168; polyhedral realization; Euclidean 3-space; icosahedron; quintic equation | 0 |
automorphism group; genus 2 surface; real algebraic curves plumbing of circle bundles over compact surfaces; 3-manifolds; classification of graph manifolds; boundaries of regular neighbourhoods of isolated singularities of complex surfaces; fundamental group of the singularity link; lens spaces; torus bundles over circ... | 0 |
automorphism group; genus 2 surface; real algebraic curves automorphisms group of Macbeath curve; algebraic curves associated with subgroups of finite index in the; modular group; non-congruence subgroups; covering of the projective line; Hurwitz group; algebraic curves associated with subgroups of finite index in the ... | 0 |
automorphism group; genus 2 surface; real algebraic curves fundamental group of the complement of a plane algebraic curve; nodal algebraic curves; computer algorithm; Zariski problem | 0 |
automorphism group; genus 2 surface; real algebraic curves relative Lie groups; algebraic curves; group of adèles; principal adèles; generalized Bäcklund transformations; Baker functions; subtori; \(\tau \) -function | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic geometry; curves of genus 1; cpencils | 0 |
automorphism group; genus 2 surface; real algebraic curves automorphism group; transitivity; flexibility; affine cone; Cox ring; Segre-Veronese embedding; secant variety; del Pezzo surface | 0 |
automorphism group; genus 2 surface; real algebraic curves simply-connected smooth projective surface; algebraic curve; normal bundle; homology group | 0 |
automorphism group; genus 2 surface; real algebraic curves error-correcting code; \(C_{ab}\) curves; towers of algebraic function fields; genus | 0 |
automorphism group; genus 2 surface; real algebraic curves normal coverings; hyperelliptic real algebraic curves; combinatorial methods | 0 |
automorphism group; genus 2 surface; real algebraic curves classification of real Enriques surfaces; Euler characteristic; real part of a real algebraic surface | 0 |
automorphism group; genus 2 surface; real algebraic curves characterization of the complex affine plane; simply connected algebraic curves; Ramanujam surfaces; hyperbolic complex analysis; regular actions of the group \({\mathbb{C}}^*\) | 0 |
automorphism group; genus 2 surface; real algebraic curves K3 surface; complex K3 surface; finite automorphism group; transcendental value; transcendental index; threefolds | 0 |
automorphism group; genus 2 surface; real algebraic curves complex multiplications; elliptic curve; Abelian varieties; algebraic period relations; diophantine approximations to numbers related to these periods; approximations to \(\pi \); hypergeometric functions; CM-varieties; modular curves; transcendence problems; m... | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic curves; convolutions; convolution degree; offsets; genus; rational curves | 0 |
automorphism group; genus 2 surface; real algebraic curves Leech lattice; \(K3\) surface; automorphism group of a \(K3\) surface; projective model of a \(K3\) surface | 0 |
automorphism group; genus 2 surface; real algebraic curves order of Brauer group; product of algebraic curves; finite ground field | 0 |
automorphism group; genus 2 surface; real algebraic curves Chebotarev density theorem; Mordell-Weil lattices; Weyl groups; algebraic equation; Galois group; Galois extension; lines on a smooth cubic surface | 0 |
automorphism group; genus 2 surface; real algebraic curves Riemannian metric; generalized Wallach space; normalized Ricci flow; dynamical system; degenerate singular point of dynamical system; real algebraic surface; singular point of real algebraic surface | 0 |
automorphism group; genus 2 surface; real algebraic curves strong symmetric genus; automorphisms; Riemann surface; 2-group | 0 |
automorphism group; genus 2 surface; real algebraic curves rationality; complex homology; 2-cells; unimodular trees of non-singular rational curves; contractible Chow-group; trivial algebraic vector bundles | 0 |
automorphism group; genus 2 surface; real algebraic curves algebroid curves on quasihomogeneous algebraic surface; Witt ring; formal power series | 0 |
automorphism group; genus 2 surface; real algebraic curves M-curves; real pseudo-holomorphic curves; braid group | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic curves; real decomposable algebraic curves; patchworking | 0 |
automorphism group; genus 2 surface; real algebraic curves complement of algebraic curves; fundamental group; Alexander polynomial; Zariski pairs; topological type; Zariski problem | 0 |
automorphism group; genus 2 surface; real algebraic curves \(K3\) surface; Niemeier lattices; automorphism group; Picard lattice; rational curve | 0 |
automorphism group; genus 2 surface; real algebraic curves logarithmic geometry; tropical geometry; Picard group; Jacobian; algebraic curves | 0 |
automorphism group; genus 2 surface; real algebraic curves tropical geometry; patchworking; inflection points; tropical modifications; real algebraic curves | 0 |
automorphism group; genus 2 surface; real algebraic curves pro-\(\ell\) fundamental group of an algebraic curve; automorphism group; linear Galois-representations; generalized Jacobian varieties; finite coverings | 0 |
automorphism group; genus 2 surface; real algebraic curves phylogenetics; group-based models; maximum likelihood estimation; real algebraic geometry; numerical algebraic geometry; algebraic statistics | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic surface; vector bundle; parabolic vector bundle; monodromy group | 0 |
automorphism group; genus 2 surface; real algebraic curves moduli of vector bundles; algebraic curve; real algebraic geometry; Brauer group; stack | 0 |
automorphism group; genus 2 surface; real algebraic curves complex projective variety; Hilbert scheme; codimension two subvariety not of general type; Néron-Severi group; algebraic homology class; arithmetic genus; geometric genus; Castelnuovo-Halphen theory | 0 |
automorphism group; genus 2 surface; real algebraic curves action of real algebraic group; real algebraic variety; real analytic variety; quotient | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic curve; elliptic curve; algebraic surface; Shimura variety; arithmetic group; Picard modular group; Gauss numbers; congruence numbers; Kähler-Einstein metric; negative constant curvature; unit ball | 0 |
automorphism group; genus 2 surface; real algebraic curves non-algebraic surface; complex torus; holomorphic vector bundle; Neron- Severi group; 2-dimensional complex torus; compact complex surface; topological vector bundle | 0 |
automorphism group; genus 2 surface; real algebraic curves positive polynomials; real algebraic curves; real algebraic surfaces; patchworking | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic curve over a finite field; group of automorphisms; rational group ring; zeta-functions of the quotient curves | 0 |
automorphism group; genus 2 surface; real algebraic curves generic position; topology of real algebraic curves | 0 |
automorphism group; genus 2 surface; real algebraic curves group of biregular automorphisms; complex K3 surfaces; nodal curves on a K3-like surface; anticanonical basic surface | 0 |
automorphism group; genus 2 surface; real algebraic curves entire holomorphic curves in surfaces; algebraic degeneracy; Bloch conjecture; irregularity; surface of general type; no nonconstant entire curve; Kobayashi hyperbolic | 0 |
automorphism group; genus 2 surface; real algebraic curves p-rank of a curve; order of automorphism group of a curve; coverings of curves; p-Sylow subgroup; ramification group; Hurwitz inequality | 0 |
automorphism group; genus 2 surface; real algebraic curves Riemann surface; holomorphic mapping; anticonformal involution; real curve; conformal automorphism | 0 |
automorphism group; genus 2 surface; real algebraic curves absolute Galois group; outer automorphism group of the pro-\(\ell\) fundamental group of the punctured projective line; Elliptic curves; modular curves | 0 |
automorphism group; genus 2 surface; real algebraic curves \(K3\) surface; Picard lattice; automorphism group; rational curve; degeneration; integer symmetric bilinear form | 0 |
automorphism group; genus 2 surface; real algebraic curves quotient of real algebraic set; finite group action | 0 |
automorphism group; genus 2 surface; real algebraic curves automorphism group; non-singular cubic surface | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic curve; finite field; maximal curves; genus | 0 |
automorphism group; genus 2 surface; real algebraic curves \(K3\) surface; uniqueness; non-symplectic automorphism; Picard group | 0 |
automorphism group; genus 2 surface; real algebraic curves algebraic biregular automorphism group of four-dimensional affine space | 0 |
automorphism group; genus 2 surface; real algebraic curves elliptic curves; algebraic curves; group schemes; modular functions; \(L\)-functions; theta functions; Fermat's last theorem; conjecture of Birch and Swinnerton-Dyer; Shimura-Taniyama-Weil conjecture; Calabi-Yau varieties; string theory; cryptography; Hopf alge... | 0 |
automorphism group; genus 2 surface; real algebraic curves Algebraic curves; genus; adjoint curve; moduli | 0 |
automorphism group; genus 2 surface; real algebraic curves upper bound; heights of integer points; algebraic curves; Mordell-Weil group | 0 |
automorphism group; genus 2 surface; real algebraic curves real algebraic groups; complexifications; maximal tori; solvable linear groups; group actions | 0 |
automorphism group; genus 2 surface; real algebraic curves abelian varieties; algebraic curves; arithmetic Fuchsian groups; Hecke operators; automorphic forms; zeta-functions; automorphic functions; elliptic curves; complex multiplication; cohomology group; congruence relations; modular correspondences | 0 |
automorphism group; genus 2 surface; real algebraic curves compact bordered Klein surface; maximal symmetry; topological type; species of genus; \(M^*\)-group; full covering; fully wound covering; \(M^*\)-simple group | 0 |
automorphism group; genus 2 surface; real algebraic curves number of automorphisms; algebraic curve; automorphism group | 0 |
automorphism group; genus 2 surface; real algebraic curves Brauer groups; moduli of elliptic curves; Brauer group of algebraic stacks | 0 |
automorphism group; genus 2 surface; real algebraic curves enumerative geometry; number of real plane curves; \(M\)-curves; Picard group; \((M-1)\)-curves; real space curves; enumeration of curves | 0 |
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