Spin Curves Over Nonstable Curves

Spin Curves over Non-stable Curves

Here we consider degenerations of stable spin curves for a fixed smoothing of a non-stable curve: we are able to give enumerative results and a description of limits of stable spin curves. We give a geometrically meaningful definition of spin curves over non-stable curves.

Spin Structures over Non Stable Curves

Here we consider degenerations of stable spin structures when a smoothing of a non stable curve is fixed. We are able to give enumerative results and a geometric description of spin structures over non stable curves using twisted spin curves.

Enriched Spin Curves on Stable Curves with Two Components

In [M], Mainò constructed a moduli space for enriched stable curves, by blowing-up the moduli space of Deligne-Mumford stable curves. We introduce enriched spin curves, showing that a parameter space for these objects is obtained by blowing-up the moduli space of spin curves.

Elliptic Curves over Q

All polynomials and rational functions in this essay are assumed to have coefficients in Q . Fix an integer n ≥ 1. An affine variety is a simultaneous irreducible system of polynomial equations in n variables. The Q -points, R -points and C points of the affine variety are all solutions of the polynomial system in Q , R n and C , respectively. Rational projective n-spaceg Q n is the set of line...

Elliptic Curves over Q