PARTIAL FOURIER-MUKAI TRANSFORM FOR INTEGRABLE SYSTEMS WITH APPLICATIONS TO HITCHIN FIBRATION

摘要

Let X be an abelian scheme over a scheme B. The Fourier-Mukai transform gives an equivalence between the derived category of X and the derived category of the dual abelian scheme. We partially extend this to certain schemes X over B (which we call degenerate abelian schemes) whose generic fiber is an abelian variety, while special fibers are singular.