Algebra & Number Theory

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

Emanuele Macrì

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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

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

Received: 30 July 2012
Revised: 10 June 2013
Accepted: 11 June 2013
First available in Project Euclid: 20 December 2017

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Secondary: 18E30: Derived categories, triangulated categories 14J30: $3$-folds [See also 32Q25]

Bridgeland stability conditions derived category Bogomolov–Gieseker inequality


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.

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