Special triple covers of algebraic surfaces
Special triple covers of algebraic surfaces
We study special triple covers f:T\to S of algebraic surfaces, where the Tschirnhausen bundle \mathcal{E}=\left(f_*\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 …