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Advances in Geometry

Managing Editor: Grundhöfer, Theo / Joswig, Michael

Editorial Board: Bamberg, John / Bannai, Eiichi / Cavalieri, Renzo / Coskun, Izzet / Duzaar, Frank / Eberlein, Patrick / Gentili, Graziano / Henk, Martin / Kantor, William M. / Korchmaros, Gabor / Kreuzer, Alexander / Lagarias, Jeffrey C. / Leistner, Thomas / Löwen, Rainer / Ono, Kaoru / Ratcliffe, John G. / Scheiderer, Claus / Van Maldeghem, Hendrik / Weintraub, Steven H. / Weiss, Richard


IMPACT FACTOR 2018: 0.789

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Continuous CM-regularity of semihomogeneous vector bundles

Alex Küronya / Yusuf Mustopa
  • Corresponding author
  • Tufts University, Department of Mathematics, Bromfield-Pearson Hall, 503 Boston Avenue, Medford, MA 02155, USA
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Published Online: 2019-06-30 | DOI: https://doi.org/10.1515/advgeom-2019-0011

Abstract

We ask when the CM (Castelnuovo–Mumford) regularity of a vector bundle on a projective variety X is numerical, and address the case when X is an abelian variety. We show that the continuous CM-regularity of a semihomogeneous vector bundle on an abelian variety X is a piecewise-constant function of Chern data, and we also use generic vanishing theory to obtain a sharp upper bound for the continuous CM-regularity of any vector bundle on X. From these results we conclude that the continuous CM-regularity of many semihomogeneous bundles — including many Verlinde bundles when X is a Jacobian — is both numerical and extremal.

Keywords: Vector bundle; Castelnuovo–Mumford regularity

MSC 2010: 14F05

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About the article

Received: 2018-02-19

Revised: 2018-04-12

Published Online: 2019-06-30


Communicated by: I. Coskun


Citation Information: Advances in Geometry, ISSN (Online) 1615-7168, ISSN (Print) 1615-715X, DOI: https://doi.org/10.1515/advgeom-2019-0011.

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