Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces

By M. Aprodu, G. Farkas, A. Ortega. 2012

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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.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d1d723dfb7aecffb3ef5a6f0d177a991c8bee67a

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In Algebra and Number Theory

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In Computational Theory and Mathematics

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In Geometry and Topology

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  2. Claire Voisin
  3. Charles Vial
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  6. D. Huybrechts
  7. Samuel Boissière
  8. A. Sarti

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