## Algebra & Number Theory

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

Emanuele Macrì

#### 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.

#### Article information

Source
Algebra Number Theory, Volume 8, Number 1 (2014), 173-190.

Dates
Revised: 10 June 2013
Accepted: 11 June 2013
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.ant/1513730138

Digital Object Identifier
doi:10.2140/ant.2014.8.173

Mathematical Reviews number (MathSciNet)
MR3207582

Zentralblatt MATH identifier
1308.14016

#### Citation

Macrì, Emanuele. A generalized Bogomolov–Gieseker inequality for the three-dimensional projective space. Algebra Number Theory 8 (2014), no. 1, 173--190. doi:10.2140/ant.2014.8.173. https://projecteuclid.org/euclid.ant/1513730138

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