Wedderburn components, the index theorem and continuous Castelnuovo-Mumford regularity for semihomogeneous vector bundles

Abstract We study the property of continuous Castelnuovo-Mumford regularity , for semihomogeneous vector bundles over a given Abelian variety, which was formulated in A. Küronya and Y. Mustopa [Adv. Geom. 20 (2020), no. 3, 401-412]. Our main result gives novel description thereof. It is expressed terms certain normalized polynomial functions that are obtained via Wedderburn decomposition variety’s endo-morphism algebra. This builds on earlier work Mumford Kempf applies form Riemann-Roch Theorem established N. Grieve [New York J. Math. 23 (2017), 1087-1110]. In complementary direction, we explain how these topics pertain to Index Generic Vanishing Theory conditions simple bundles. doing so, refine results from M. Gulbrandsen [Matematiche (Catania) 63 (2008), 1, 123–137], [Internat. 25 (2014), 4, 1450036, 31] D. [Questions Algebraic Varieties (C.I.M.E., III Ciclo, Varenna, 1969), Edizioni Cremonese, Rome, 1970, pp. 29-100].