Special triple covers of algebraic surfaces

Abstract

We study special triple covers $f:T\to S$ of algebraic surfaces, where the Tschirnhausen bundle $\mathcal{E}={\left(f_{\ast }{\mathcal{O}}_T/{\mathcal{O}}_S\right)}^{\vee }$ is a quotient of a split rank three vector bundle, and we provide several necessary and sufficient criteria for the existence. As an application, we give a complete classification of special triple planes, finding among others two nice families of K3 surfaces.

arXiv comment26 pages