Rank 2 Ulrich bundles on general double plane covers

TL;DR

This paper proves that general double covers of the projective plane ramified along smooth curves of degree at least 6 support special rank 2 Ulrich bundles, expanding understanding of vector bundles on such surfaces.

Contribution

It establishes the existence of rank 2 special Ulrich bundles on general double plane covers ramified along smooth curves of degree 2s for s ≥ 3.

Findings

Existence of rank 2 Ulrich bundles on these covers.

Supports conjectures about Ulrich bundles on branched covers.

Advances classification of vector bundles on algebraic surfaces.

Abstract

We prove that a double cover of $\mathbb{P}^2$ ramified along a general smooth curve B of degree $2s$, for $s \geq 3$, supports a rank 2 special Ulrich bundle.