Effective global generation on varieties with numerically trivial canonical class

Abstract

We prove a Fujita-type theorem for varieties with numerically trivial canonical bundle using properties of semihomogeneous bundles on abelian varieties. We combine our results with work of Riess on compact hyperkähler manifolds and work of Mukai, Pareschi and Yoshioka to obtain effective global generation statements for certain moduli spaces of sheaves on abelian surfaces. Among these is the statment that if $\cL$ is an ample line bundle on the Hilbert square $S^{[2]}$ of an abelian surface $S,$ then $\cL^{\otimes m}$ is globally generated for $m\ge 3.$

The proof of Theorem A has been substantially revised. Since the proof of Theorem A no longer depends on the analytic results from v4, the latter have been removed

References in corpus (2)

• Hodge metrics and the curvature of higher direct images
• Fourier-Mukai transforms of line bundles on derived equivalent abelian varieties