Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces

Marian Aprodu; Gavril Farkas; Angela Ortega

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arXiv · 1212.6248

Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces

Marian Aprodu·Gavril Farkas·Angela Ortega

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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.

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Marian Aprodu, Gavril Farkas, Angela Ortega. 2012-12-26. Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces. https://arxiv.org/abs/1212.6248

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