Bridgeland stability conditions on normal surfaces
Adrian Langer
TL;DR
This paper establishes a new Bogomolov inequality for normal proper surfaces, enabling the construction of Bridgeland stability conditions on these surfaces, including non-projective schemes, thus expanding the scope of stability conditions in algebraic geometry.
Contribution
It introduces a novel Bogomolov inequality for normal surfaces and constructs Bridgeland stability conditions on non-projective, proper schemes, a first in the field.
Findings
New Bogomolov inequality for normal surfaces
Construction of Bridgeland stability conditions on non-projective schemes
First known examples of stability conditions on such schemes
Abstract
We prove a new version of Bogomolov's inequality on normal proper surfaces. This allows to construct Bridgeland's stability condition on such surfaces. In particular, this gives the first known examples of stability conditions on non-projective, proper schemes.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Matrix Theory and Algorithms · Advanced Mathematical Modeling in Engineering