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

Thomas Krämer

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arXiv · 1604.02389

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

Thomas Krämer

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Abstract

We propose two new approaches to the Tannakian Galois groups of holonomic D-modules on abelian varieties. The first is an interpretation in terms of principal bundles given by the Fourier-Mukai transform, which shows that they are almost connected. The second constructs a microlocalization functor relating characteristic cycles to Weyl group orbits of weights. This explains the ubiquity of minuscule representations, and we illustrate it with a Torelli theorem and with a bound for decompositions of a given subvariety as a sum of subvarieties. The appendix sketches a twistor variant that may be useful for D-modules not coming from Hodge theory.

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Thomas Krämer. 2016-04-08. Characteristic cycles and the microlocal geometry of the Gauss map, I. https://arxiv.org/abs/1604.02389

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