Ample Weil divisors
Alberto Chiecchio, Stefano Urbinati
TL;DR
This paper develops a framework for understanding positivity properties of Weil divisors on normal projective varieties, providing characterizations, cohomology theorems, and applications to log Fano varieties.
Contribution
It introduces new definitions and results for positivity of Weil divisors, extending classical concepts to a broader class of divisors on singular varieties.
Findings
Characterizations of positivity properties for Weil divisors
Vanishing and non-vanishing theorems for cohomology
Global generation results and applications to log Fano varieties
Abstract
We define and study positivity (nefness, amplitude, bigness and pseudo-effectiveness) for Weil divisors on normal projective varieties. We prove various characterizations, vanishing and non-vanishing theorems for cohomology, global generation statements, and a result related to log Fano.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds