D-modules on 1|1 Supercurves
arXiv:0908.1989 · doi:10.1016/j.geomphys.2009.12.016
Abstract
It is known that to every 1|1 dimensional supercurve X there is associated a dual supercurve \hat{X}, and a superdiagonal Δin their product. We establish that the categories of D-modules on X, \hat{X}, and Δare 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.
18 pages