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

2016/04/08 by Thomas Krämer, Krämer, Thomas · 1 citation
Mathematics · #14F10 #14K12 (Primary) #18D10 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Differential Geometry (math.DG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.1604.02389

openalex publication_date 2016/04/08 · openalex created_date 2022/12/15 · openalex updated_date 2026/07/28

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.

Cited by

• E₆-local systems from cubic threefolds

Related

• Holonomic D-modules on abelian varieties
• Cycle caracéristique pour les D-modules coadmissibles sur une courbe formelle
• Holonomic complexes on abelian varieties, Part I
• Sheaves with connection on abelian varieties
• Characteristic cycles associated to holonomic \mathscr D-modules