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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

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

IMPACT FACTOR 2018: 1.859

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1435-5345
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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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• Other articles by this author:
/ Gavril Farkas
/ Angela Ortega
Published Online: 2015-02-27 | DOI: https://doi.org/10.1515/crelle-2014-0124

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 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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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,

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© 2017 Walter de Gruyter GmbH, Berlin/Boston.

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