Special Ulrich bundles on non-special surfaces with $p_g=q=0$

Gianfranco Casnati

Published 2016-09-26Version 1

Let $S$ be a surface with $p_g(S)=q(S)=0$ and endowed with a very ample line bundle $\mathcal O_S(h)$ such that $h^1\big(S,\mathcal O_S(h)\big)=0$. We show that $S$ supports special Ulrich bundles of rank $2$, extending a recent result by A. Beauville. Moreover, we also show that if such an $S$ is minimal with non-negative Kodaira dimension, then it supports families of dimension $p$ of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large $p$.