D-modules on 1|1 Supercurves

Details D-modules on 1|1 Supercurves D-modules on 1|1 Supercurves

2009-08-13

arxiv.org/abs/0908.1989v1

Mathematics

Algebraic Geometry

18 pages

Scientific paper

It is known that to every 1|1 dimensional supercurve X there is associated a dual supercurve \hat{X}, and a superdiagonal \Delta in their product. We establish that the categories of D-modules on X, \hat{X}, and \Delta are equivalent. This follows from a more general result about D-modules and purely odd submersions. The equivalences preserve tensor products, and take vector bundles to vector bundles. Line bundles with connection are studied, and examples are given where X is a superelliptic curve.

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