Demailly's Conjecture and the Containment Problem
Commutative Algebra
2021-06-17 v3 Algebraic Geometry
Abstract
We investigate Demailly's Conjecture for a general set of sufficiently many points. Demailly's Conjecture generalizes Chudnovsky's Conjecture in providing a lower bound for the Waldschmidt constant of a set of points in projective spaces. We also study a containment between symbolic and ordinary powers conjectured by Harbourne and Huneke that in particular implies Demailly's bound, and prove that a general version of that containment holds for generic determinantal ideals and defining ideals of star configurations.
Keywords
Cite
@article{arxiv.2009.05022,
title = {Demailly's Conjecture and the Containment Problem},
author = {Sankhaneel Bisui and Eloísa Grifo and Huy Tài Hà and Thái Thành Nguyên},
journal= {arXiv preprint arXiv:2009.05022},
year = {2021}
}
Comments
v3 changes: improved the containments shown for ideals of minors of generic matrices, minors of generic symmetric matrices, and pfaffians of generic skew symmetric matrices