Characteristic cycles and the microlocal geometry of the Gauss map, II

Abstract

We show that for the reductive Tannaka groups of semisimple holonomic $\mathcal{D}$-modules on abelian varieties, every Weyl group orbit of weights of their universal cover is realized by a conic Lagrangian cycle on the cotangent bundle. Applications include a weak solution to the Schottky problem in genus five, an obstruction for the existence of summands of subvarieties on abelian varieties and a criterion for the simplicity of the arising Lie algebras.

38 pages, comments welcome

References in corpus (5)

• Cubic threefolds, Fano surfaces and the monodromy of the Gauss map
• Decomposable theta divisors and generic vanishing
• The degree of the Gauss map of the theta divisor
• Generic vanishing and minimal cohomology classes on abelian fivefolds
• Summands of theta divisors on Jacobians