Higher Gaussian Maps on K3 Surfaces

Abstract

Abstract We give sufficient conditions for the surjectivity of higher Gaussian maps on a polarized K3 surface. As an application, we show that the $k$-th Gaussian map for a general curve of genus $g$ (that depends quadratically with $k$) is surjective. Along the proof, we also exhibit an ampleness criterion for divisors in the Hilbert scheme of two points of a K3 surface.