Ulrich bundles on ruled surfaces

Abstract

In this short note, we study the existence problem for Ulrich bundles on ruled surfaces, focusing our attention on the smallest possible rank. We show that existence of Ulrich line bundles occurs if and only if the coefficient $\alpha$ of the minimal section in the numerical class of the polarization equals one. For other polarizations, we prove the existence of rank two Ulrich bundles.

References in corpus (3)

• Ulrich bundles on surfaces with $q=p_g=0$
• Ulrich line bundles on Enriques surfaces with a polarization of degree four
• Ulrich bundles on blowups

Cited by in corpus (7)

• Characterization of Ulrich bundles on Hirzebruch surfaces
• Ulrich Bundles on Projective Spaces
• On Ulrich bundles on projective bundles
• Ulrich line bundles on double planes
• On the existence of Ulrich bundles on blown-up varieties at a point
• Ulrich bundles on the degree six Segre fourfold
• On the existence of Ulrich bundles on geometrically ruled surfaces