Demailly's Conjecture and the Containment Problem

Authors

Sankhaneel Bisui, Tulane UniversityFollow
Eloisa Grifo, University of Nebraska-LincolnFollow
Huy Tài Hà, Tulane UniversityFollow
Thái Thành Nguyên, Tulane UniversityFollow

Date of this Version

6-2021

Citation

arXiv:2009.05022v3 [math.AC] 15 Jun 2021

Comments

Copyright © 2021 the authors

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 space. 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.