A generalized Bogomolov–Gieseker inequality for the three-dimensional projective space

Macrì, Emanuele

doi:10.2140/ant.2014.8.173

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A generalized Bogomolov–Gieseker inequality for the three-dimensional projective space

Emanuele Macrì

Vol. 8 (2014), No. 1, 173–190

DOI: 10.2140/ant.2014.8.173

Abstract

A generalized Bogomolov–Gieseker inequality for tilt-stable complexes on a smooth projective threefold was conjectured by Bayer, Toda, and the author. We show that such inequality holds true in general if it holds true when the polarization is sufficiently small. As an application, we prove it for the three-dimensional projective space.

Keywords

Bridgeland stability conditions, derived category, Bogomolov–Gieseker inequality

Mathematical Subject Classification 2010

Primary: 14F05

Secondary: 18E30, 14J30

Milestones

Received: 30 July 2012

Revised: 10 June 2013

Accepted: 11 June 2013

Published: 20 April 2014

Authors

Emanuele Macrì
Department of Mathematics The Ohio State University 231 West 18th Avenue Columbus, OH 43210-1174 United States

Vol. 8, No. 1, 2014