Higher Gaussian Maps on K3 surfaces

TL;DR

This paper investigates the surjectivity of higher Gaussian maps on polarized K3 surfaces and applies these results to show surjectivity for higher Gauss maps of general curves of genus g.

Contribution

It provides necessary conditions for the surjectivity of higher Gaussian maps on K3 surfaces and demonstrates surjectivity for general curves of genus g depending quadratically on k.

Findings

Necessary conditions for surjectivity of higher Gaussian maps on K3 surfaces

Surjectivity of higher k-th Gauss map for general curves of genus g

Quadratic dependence of genus g on k for surjectivity

Abstract

We give necessary conditions for the surjectivity of the higher Gaussian maps on a polarized K3 surface. As an application, we show that the higher $k$-th Gauss map for a general curve of genus $g$ (that depends quadratically with $k$) is surjective.