Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces

Abstract

The Minimal Resolution Conjecture (MRC) for points on a projective variety X predicts that the Betti numbers of general sets of points in X are as small as the geometry (Hilbert function) of X allows. To a large extent, we settle this conjecture for a curve C with general moduli. We show that, independently of the genus, MRC holds for a general linear system of degree d and dimension r on C if and only if d>2r-1. We then proceed to find a full solution to the Ideal Generation Conjecture for curves with general moduli. In a different direction, we prove that K3 surfaces admit Ulrich bundles of every rank. We apply this to describe a pfaffian equation for the Chow form of a K3 surface.

23 pages, final version. To appear in Crelle

References in corpus (2)

• The geometry of Ulrich bundles on del Pezzo surfaces
• ACM bundles on cubic surfaces

Cited by in corpus (10)

• Ulrich bundles on ruled surfaces
• Equivariant Ulrich bundles on exceptional homogeneous varieties
• An introduction to Ulrich bundles
• Stability of Rank 2 Ulrich Bundles on Projective K3 Surfaces
• On Ulrich bundles on projective bundles
• Ulrich Bundles on Projective Spaces
• Ulrich bundles on blowups
• Positive Ulrich Sheaves
• Counterexamples to Mercat's Conjecture
• Ulrich bundles on rational surfaces with an anticanonical pencil