# Tagged Questions

0answers
39 views

### $C^{\infty}$ 1-form on a Riemann surface is unique.

Let $X$ be a Riemann surface and $\mathcal{A}$ be a complex atlas on $X$. Suppose that $C^{\infty}$ 1-forms are given for each chart of $\mathcal{A}$, which transform to each other on their common ...
2answers
220 views

### Can there be a point on a Riemann surface such that every rational function is ramified at this point?

Let $X$ be a compact connected Riemann surface, and let $S\subset X$ be a finite subset. Does there exist a morphism $f:X\to \mathbf{P}^1(\mathbf{C})$ which is unramified at the points of $S$? I'm ...
1answer
121 views

### Modular functions of weight zero

The following question was suggested by Sasha's answer to the following question : Is the derivative of a modular function a modular function . Question. What are the modular functions with respect ...
0answers
277 views

### An argument on page 62 of Griffith's book,  “Introduction to Algebraic Curves”

I am a bit confused about some of the things that Griffiths says on page 62 of his book, Introduction to Algebraic Curves. I am not sure how I can reproduce the text here. I can see that GoogleBooks ...
0answers
86 views

### Singularity type and number of irreducible local analytic curve components

Let $V$ be an irreducible complex plane algebraic curve, $V=V(f)$, and let $\mathcal{O}_p$ be the local ring of holomorphic functions defined in some neighborhood of $p$. If $p=(0,0)$ is a smooth ...
0answers
257 views

### The Milnor Conjecture on the Unknotting Number of a Torus Knot

Let $f \colon (\mathbb{C}^{n},\mathbf{0}) \to (\mathbb{C},0)$ be a complex analytic function with isolated critical point at the origin. Define the singular hypersurface \$V_{f, \kappa} = ...
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