D-modules on 1|1 Supercurves
Abstract
It is known that to every 1|1 dimensional supercurve X there is associated a dual supercurve X, and a superdiagonal in their product. We establish that the categories of D-modules on X, X, and 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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