14
votes
0answers
592 views

New(?) reciprocity law

Consider three functions $f, g$ and $h$ on a smooth curve $X$ over $\mathbb{C}$. I have found the following equality: $$\sum (res(f\frac{dg}{g})\frac{dh}{h}-res(f\frac{dh}{h})\frac{dg}{g})=0.$$ Here ...
1
vote
0answers
123 views

Hopf lemma for line bundles on curves in algebraic geometry

In the paper http://arxiv.org/pdf/math/0110256v1.pdf Claire Voisin proves that all linear subspaces which lie inside of a (not too big) secant variety of a smooth projective curve must lie inside one ...
5
votes
2answers
637 views

“Arithmetic genus” of a plane curve singularity.

I believe that the following questions are very basic, but I don't know how to get a reference. Consider a curve in the plane $C\in \mathbb C^2$ with a singularity at $0$ and suppose it is ...
3
votes
1answer
407 views

Name for curve?

I am doing something with the curve given parametrically by $y = (-ar+b) r$, $x = \sqrt{r^2-y^2}$ for $r\in \lbrack (b-1)/a,b/a\rbrack$. It is nice enough (and of low enough degree) that I suspect ...
1
vote
1answer
179 views

invariants of plane quartics

Does anybody know a good reference where the invariants for plane quartic curves are developed?
7
votes
0answers
397 views

Elementary proof of the Hurwitz formula

I am aware of two forms of the Hurwitz formula. The first is more common, and deals only with the degrees. So if $f:X \rightarrow Y$ is a non-constant map of degree $n$ between two projective ...
1
vote
1answer
153 views

pull back of hodge bundle via glueing map

Hi, I need a precise reference for the following fact, which is certainly well known, but I do not find any. I consider the natural glueing map of pointed curves $\overline{M}_{g_1,n}\times ...
3
votes
0answers
209 views

Igusa-Clebsch invariants

I am looking for a good reference for definitions and basic properties of the Igusa-Clebsch invariants for curves of genus $2$ (especially, but not only, in positive characteristic).
2
votes
2answers
329 views

Recognize this plane curve?

An aspect of my work led to a plane curve with implicit equation $$ x^2+y^2 = 3 (y/2)^{2/3} + 1 $$ Actually, I started with the parametrization below and derived from it the equation above: ...
9
votes
0answers
438 views

Function fields of characteristic p modular curves, and mod p reductions of the classical modular equation

Let l and p be distinct primes, l>2. There are "characteristic p modular curves" X_0(l) and X(l), defined over an algebraic closure, K, of Z/p, solving moduli problems for elliptic curves with some ...
1
vote
2answers
440 views

Weil bound for characters sums. (reference-request )

Do you know on any good reference on Weil bound for charcter sums over algebraic curves. I prefer reference which assume few previous knowlage.
1
vote
3answers
609 views

Are the arithmetic genera of Cohen-Macaulay curves in a fixed homology class bounded?

Let X be a smooth projective variety over the complex numbers. Recall that a Cohen-Macaulay curve is a one-dimensional closed subscheme without embedded or isolated points (fat components are ...