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Journal für die reine und angewandte Mathematik

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Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

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Volume 2017, Issue 730


Minimal resolutions, Chow forms and Ulrich bundles on K3 surfaces

Marian Aprodu
  • Institute of Mathematics “Simion Stoilow”, Romanian Academy, Calea Griviţei 21, Sector 1, 010702 Bucharest, Romania; and Faculty of Mathematics and Computer Science, University of Bucharest, 14 Academiei Str., 010014 Bucharest, Romania
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/ Gavril Farkas / Angela Ortega
Published Online: 2015-02-27 | DOI: https://doi.org/10.1515/crelle-2014-0124


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 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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About the article

Received: 2014-02-22

Revised: 2014-10-15

Published Online: 2015-02-27

Published in Print: 2017-09-01

The first author was partly supported by the CNCS-UEFISCDI grant PN-II-PCE-2011-3-0288 and by a Humboldt fellowship. The second and third authors were partly supported by the SFB 647 “Raum-Zeit-Materie”.

Citation Information: Journal für die reine und angewandte Mathematik, Volume 2017, Issue 730, Pages 225–249, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2014-0124.

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