Continuous CM-regularity of semihomogeneous vector bundles

2017/03/21 by Küronya, Alex, Mustopa, Yusuf
#14K05 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.07237

Abstract

We show that if X is an abelian variety of dimension g ≥ 1 and \mathcal E is an M-regular coherent sheaf on X, the Castelnuovo-Mumford regularity of \mathcal E with respect to an ample and globally generated line bundle \mathcal O(1) on X is at most g, and that equality is obtained when \mathcal E^\vee(1) is continuously globally generated. As an application, we give a numerical characterization of ample semihomogeneous vector bundles for which this bound is attained.

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