Ulrich line bundles on double planes

Abstract

Consider a smooth complex surface $X$ which is a double cover of the projective plane ${\mathbb{P}}^2$ branched along a smooth curve of degree $2s$. In this article, we study the geometric conditions which are equivalent to the existence of Ulrich line bundles on $X$ with respect to this double covering. Also, for every $s\ge 1$, we describe the classes of such surfaces which admit Ulrich line bundles and give examples.

18 pages, journal version, the statement of Theorem 1.1 has been changed

References in corpus (2)

• Ulrich bundles on ruled surfaces
• Ulrich line bundles on Enriques surfaces with a polarization of degree four