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Results tagged with algebraic-curves
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user 40038
for questions on one dimensional algebraic varieties over any field, including questions of moduli, and questions about specific curves.
8
votes
2
answers
1k
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The gonality of smooth plane curves
I have often seen the assertion that for a smooth plane curve $C$ of degree $d$ the gonality of $C$ is $d-1$ and each gonality pencil is obtained by projection from a point of $C$ onto a line.
(let m …
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3
votes
2
answers
404
views
Are curves with maximal Clifford index Brill-Noether general?
By the Brill-Noether Theorem, a general curve $C$ of genus $g\geq2$ has maximal Clifford index $\lfloor \frac{g-1}{2}\rfloor$. Hence a very naive question is:
(Q1) Is a curve with maximal Clifford in …
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3
votes
0
answers
114
views
Projective normality of residual pencils on a general curve
Let $C$ be a general curve, say of even genus $g=2s$. Then $C$ has finitely many pencils $|L|$ of degree $\deg L=[g+3]/2=s+1$. Choose one such. The residual series is of degree $\deg(K_C-L)=3s-3$.
I …
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3
votes
1
answer
358
views
Existence of pencils on some special curves of genus 10
Everything over $\Bbb{C}$. Say we have a smooth curve $C$ of genus $10$ which is a double cover of a smooth plane cubic curve. Therefore $C$ admits a 1-dimensional family of pencils of degree 4 (arisi …
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2
votes
1
answer
180
views
Does $\omega_C\simeq N_{C/S}$ always happen on Enriques surfaces?
Let $S$ be an Enriques surface and $C\subset S$ a smooth irreducible curve of genus $g$.
Consider the condition $$\omega_C\simeq N_{C/S}$$
For example, when $g=1$ then $\omega_C=\mathcal{O}_C$ and th …
- 761
2
votes
1
answer
186
views
When is the Clifford index of a curve computed by pencils?
Under which circumstances is the Clifford index of a curve computed by pencils?
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