Semicontinuity of Gauss maps and the Schottky problem

Abstract We show that the degree of Gauss maps on abelian varieties is semicontinuous in families, and we study its jump loci. As an application obtain case theta divisors this answers Schottky problem. Our proof computes by specialization Lagrangian cycles cotangent bundle. also get similar results for intersection cohomology with a finite morphism to variety; it follows many components Andreotti–Mayer loci, including locus, are part stratification moduli space ppav’s defined topological type divisor.