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

Thomas Krämer 1
  • 1 Institut für Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany
Thomas Krämer
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  • Institut für Mathematik, Humboldt Universität zu Berlin, Unter den Linden 6, 10099, Berlin, Germany
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Abstract

We show that any Weyl group orbit of weights for the Tannakian group of semisimple holonomic 𝒟-modules on an abelian variety is realized by a Lagrangian cycle on the cotangent bundle. As applications we discuss 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.

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