On the Bogomolov–Gieseker Inequality in Positive Characteristic-Reference-Cited by-同舟云学术

On the Bogomolov–Gieseker Inequality in Positive Characteristic

Published:2022-09-22 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Koseki Naoki¹

Affiliation:

1. School of Mathematics , University of Edinburgh, JCMB, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK

Abstract

Abstract We prove a version of the Bogomolov–Gieseker (BG) inequality on smooth projective surfaces of general type in positive characteristic. Our result is stronger than a similar theorem by Langer for vector bundles of sufficiently large rank. Our inequality enables us to construct Bridgeland stability conditions with the full support property on all smooth projective surfaces in positive characteristic. We also prove the BG-type inequality for higher dimensional varieties.

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

https://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnac260/45972712/rnac260.pdf

Reference43 articles.

1. Bridgeland-stable moduli spaces for K-trivial surfaces;Arcara;J. Eur. Math. Soc. (JEMS),2013

2. The minimal model program for the Hilbert scheme of points on ${\mathbb {P}}^2$ and Bridgeland stability;Arcara;Adv. Math.,2013

3. Wall-crossing implies Brill-Noether: applications of stability conditions on surfaces;Bayer,2018

4. Stability conditions on Kuznetsov components;Bayer;Ann. Sci. Éc. Norm. Supér,2017

5. Brill-Noether theory for curves on generic abelian surfaces;Bayer;Pure Appl. Math. Q.,2017

Cited by 1 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Bridgeland stability conditions on normal surfaces;Annali di Matematica Pura ed Applicata (1923 -);2024-05-20