An introduction to Ulrich bundles

Abstract

After recalling the definition and basic properties of Ulrich bundles, we focus on the existence problem: does any smooth projective variety carry a Ulrich bundle? We show that the Serre construction provides a positive answer on certain surfaces and threefolds.

arXiv commentA few details added for the case of Fano threefolds

References in corpus (3)

• Determinantal hypersurfaces
• Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces
• Ulrich bundles on surfaces with $q=p_g=0$

Cited by in corpus (3)

• Ulrich bundles on non-special surfaces with $p_g=0$ and $q=1$
• Ulrich bundles on intersections of two 4-dimensional quadrics
• On the existence of Ulrich bundles on geometrically ruled surfaces