Vol. 8, No. 1, 2014

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

Emanuele Macrì

Vol. 8 (2014), No. 1, 173–190

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.

Bridgeland stability conditions, derived category, Bogomolov–Gieseker inequality
Mathematical Subject Classification 2010
Primary: 14F05
Secondary: 18E30, 14J30
Received: 30 July 2012
Revised: 10 June 2013
Accepted: 11 June 2013
Published: 20 April 2014
Emanuele Macrì
Department of Mathematics
The Ohio State University
231 West 18th Avenue
Columbus, OH 43210-1174
United States