Semi-homogeneous sheaves, Fourier–Mukai transforms and moduli of stable sheaves on abelian surfaces

摘要

This paper studies stable sheaves on abelian surfaces of Picard number one.Our main tools are semi-homogeneous sheaves and Fourier-Mukai transforms. Weintroduce the notion of semi-homogeneous presentation and investigate thebehavior of stable sheaves under Fourier-Mukai transforms. As a consequence, anaffirmative proof is given to the conjecture proposed by Mukai in the 1980s.This paper also includes an explicit description of the birationalcorrespondence between the moduli spaces of stable sheaves and the Hilbertschemes.