# Tagged Questions

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### 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 ...
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### How to induce infinitesimal deformations on curves

Let $C_1, C_2$ be two projective curves (a scheme of pure dimension $1$) in $\mathbb{P}^3$. The Hilbert scheme of curves contains informations of deformations of curves in $\mathbb{P}^3$. The question ...
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### 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 ...
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### “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 ...
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### 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 ...
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### invariants of plane quartics

Does anybody know a good reference where the invariants for plane quartic curves are developed?
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### 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 ...
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### 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: ...
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### 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 ...