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Advances in Geometry

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Continuous CM-regularity of semihomogeneous vector bundles

Alex Küronya / Yusuf Mustopa
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  • 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


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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