Chudnovsky's Conjecture and the stable Harbourne-Huneke containment

Authors

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

Document Type

Article

Date of this Version

6-2021

Citation

arXiv:2004.11213v3 [math.AC] 15 Jun 2021

Comments

Copyright © 2021 by the authors

Abstract

We investigate containment statements between symbolic and ordinary powers and bounds on the Waldschmidt constant of defining ideals of points in projective spaces. We establish the stable Harbourne conjecture for the defining ideal of a general set of points. We also prove Chudnovsky’s Conjecture and the stable version of the Harbourne–Huneke containment conjectures for a general set of sufficiently many points.