Higher Gaussian maps for special classes of curves

TL;DR

This paper investigates the rank of higher Gaussian maps associated with the canonical bundle for specific classes of smooth projective curves, including plane curves, curves on product surfaces, and curves on Enriques surfaces.

Contribution

It provides explicit computations of the rank of higher Gaussian maps for these special classes of curves, extending understanding of their geometric properties.

Findings

Determined the rank of higher Gaussian maps for plane curves.

Computed the rank for curves on product surfaces of two curves.

Analyzed the Gaussian maps for curves on Enriques surfaces.

Abstract

In this paper we study higher Gaussian (or Wahl) maps for the canonical bundle of certain smooth projective curves. More precisely, we determine the rank of higher Gaussian maps of the canonical bundle for plane curves, for curves contained in certain linear systems in a surface given by a product of two curves and for curves contained in a sufficiently ample line bundle on an Enriques surface.