Theodore Shifrin

The Gauss map of a genus three theta divisor

A smooth complex curve is determined by the Gauss map of the theta divisor of the Jacobian variety of the curve. The Gauss map is invariant with respect to the (-1)-map of the Jacobian. We show that for a generic genus three curve the Gauss map is locally Z/2-stable. One method of proof is to analyze the first-order Z/2-deformations of the Gauss map of a hyperelliptic theta divisor

Conic lagrangian singularities

Abstract We classify conic Lagrangian holomorphic map germs with Z 2 symmetry, in terms of homo geneous generating families. The motivating example is the Gauss map of the theta divisor of a principally polarized abelian variety.