2004/01/26 by Donu Arapura, Arapura, Donu
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Polynomial and algebraic computation #math.AG
paper · pdf · doi:10.48550/arxiv.math/0401364
The final revision (to appear in Amer. J Math) contains several corrections
openalex publication_date 2004/01/26 · arxiv created 2006/03/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is a sequel to the paper "Frobenius amplitude and strong vanishing theorems for vector bundles" (math.AG/0202129). We introduce a more elementary variant of the notion of F-amplitude from the earlier paper which we call amplitude. This provides another measure of positivity of a vector bundle which is related to a number of preexisting positivity notions such as k-ampleness or q-convexity. We use this to refine the estimates of F-amplitude from the first paper, and to deduce some further vanishing theorems as a consequence. We also give some new proofs of some known vanishing theorems for Abelian and toric varieties by analogous methods. For technical reasons, we need to develop a theory of partial Castelnuovo-Mumford regularity which provides a rough measure of the cohomological complexity of a sheaf. Since this material may have independent interest, it is contained in a section which can be read on its own.