Seshadri Regions and the Asymptotic Shape of Multigraded Regularity
Algebraic Geometry
2025-12-08 v1 Commutative Algebra
Abstract
We introduce the Seshadri region of a subvariety, a convex region packaging the classical Seshadri constants with respect to every line bundle simultaneously. We develop the theory of Seshadri regions as a measure of positivity along subvarieties and apply it to determine asymptotic Castelnuovo-Mumford regularity for ideal powers and symmetric powers on smooth projective toric varieties.
Keywords
Cite
@article{arxiv.2512.05289,
title = {Seshadri Regions and the Asymptotic Shape of Multigraded Regularity},
author = {Juliette Bruce and Lauren Cranton Heller and Mahrud Sayrafi and Alexandra Seceleanu},
journal= {arXiv preprint arXiv:2512.05289},
year = {2025}
}
Comments
32 pages, 5 figures, comments very welcome!