List questions from algebraic-curves

Published on 10 May 2026 - 13:48

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Why is the first cohomology of a projective curve over an algebraically closed field a birational invariant?

Published on 10 May 2026 - 13:51

47

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Show that $\mathbb{C}^{*}$ is a hyperbolic type

Published on 10 May 2026 - 19:16

379

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Does a curve's genus depend on its base field?

Published on 16 Apr 2026 - 1:51

75

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For $M$ compact Riemann surface, divisors $D_{1}$ and $D_{2}, D_{2}\geq 0$ show that $\dim L(D_{1}+D_{2})\leq \dim L(D_{1})+\deg D_{2}$

Published on 10 May 2026 - 22:04

600

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Divisors on hyperelliptic curves

Published on 11 Apr 2026 - 10:32

87

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The space $\Omega^1(X)$ of hyperelliptic curve $X$.

Published on 11 May 2026 - 4:38

72

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A question on group law of Elliptic Curves, from Milne's Notes

Published on 10 May 2026 - 16:39

247

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How to construct a certain covering of $\mathbb P^1_{\mathbb C}$ in a weighted projective space

Published on 10 May 2026 - 15:37

455

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Extending a Cartier divisor on a curve to singular points?

Published on 10 May 2026 - 14:55

86

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Why does this method of finding the equation of the tangent line to a second-degree curve work?

Published on 10 May 2026 - 15:52

66

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Is $\Sigma$ compact if the partial derivatives of elliptic curve $P(x,y,z)$ do not all vanish at any point of $\Sigma$?

Published on 10 May 2026 - 17:50

514

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Compact Riemann surface of genus 2 as the normalization of a quartic curve.

Published on 10 May 2026 - 19:47

978

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Adjunction Formula

Published on 10 May 2026 - 19:44

1.5k

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Twists of an Elliptic Curve over Finite Fields

Published on 14 Apr 2026 - 10:54

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There Exist Exactly Two Nonisomorphic Affine Conic Plane Curves

Why is the first cohomology of a projective curve over an algebraically closed field a birational invariant?

Show that $\mathbb{C}^{*}$ is a hyperbolic type

Does a curve's genus depend on its base field?

For $M$ compact Riemann surface, divisors $D_{1}$ and $D_{2}, D_{2}\geq 0$ show that $\dim L(D_{1}+D_{2})\leq \dim L(D_{1})+\deg D_{2}$

Divisors on hyperelliptic curves

The space $\Omega^1(X)$ of hyperelliptic curve $X$.

A question on group law of Elliptic Curves, from Milne's Notes

How to construct a certain covering of $\mathbb P^1_{\mathbb C}$ in a weighted projective space

Extending a Cartier divisor on a curve to singular points?

Why does this method of finding the equation of the tangent line to a second-degree curve work?

Is $\Sigma$ compact if the partial derivatives of elliptic curve $P(x,y,z)$ do not all vanish at any point of $\Sigma$?

Compact Riemann surface of genus 2 as the normalization of a quartic curve.

Adjunction Formula

Twists of an Elliptic Curve over Finite Fields

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