Semicontinuity of Gauss maps and the Schottky problem

Abstract: We show that the degree of the Gauss map for subvarieties of abelian varieties is semicontinuous in families, and we discuss its jump loci. In the case of theta divisors this gives a finite stratification of the moduli space of ppav's whose strata include the Torelli locus and the Prym locus. More generally we obtain semicontinuity results for the intersection cohomology of algebraic varieties with a finite morphism to an abelian variety, leading to a topological interpretation for various jump loci in algebraic geometry.

This is joint work with Giulio Codogni.

mathematical physicsalgebraic geometryalgebraic topologydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic

Geometry and Physics @ Lisbon