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Results tagged with algebraic-curves
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user 110362
for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.
5
votes
1
answer
290
views
First cohomology of tangent sheaf of rational curve
Let $C$ be a reduced, connected, projective and purely one-dimensional scheme of finite type over a field $k$.
Suppose that $C$ is rational, i.e. that the normalisation of $C$ is a disjoint union of c …
- 984
5
votes
0
answers
171
views
Unirationality of universal Jacobian over special strata of moduli space of pointed genus 3 ...
Let $M_{3,1}$ be the (coarse, non-compactified) moduli space of genus $3$ curves with a marked point over a field $k$ of characteristic zero. Throwing away the hyperelliptic curves, take the open subs …
- 984
2
votes
Accepted
On degree and section of a line bundle on a smooth plane quintic
This is true, and can be shown by an induction argument on $h^0(A)$.
If $h^0(A)=2$, then $\deg(A)\geq 4$ since the gonality of $X$ is $4$.
If $h^0(A)>2$, let $p\in X$ be a point in the support of an e …
- 984
2
votes
Compactified Jacobian of a rational curve whose normalization is a set-theoretic bijection
Section 3 of the following paper of Beauville should answer your question: https://arxiv.org/abs/alg-geom/9701019
In particular, it is shown there that, up to replacing the compactified Jacobian by a …
- 984