Autoequivalences, stability conditions, and n-gons : an example of how stability conditions illuminate the action of autoequivalences associated to derived categories

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Autoequivalences, stability conditions, and n-gons : an example of how stability conditions illuminate the action of autoequivalences associated to derived categories

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Title: Autoequivalences, stability conditions, and n-gons : an example of how stability conditions illuminate the action of autoequivalences associated to derived categories
Author: Lowrey, Parker Eastin
Abstract: Understanding the action of an autoequivalence on a triangulated category is generally a very difficult problem. If one can find a stability condition for which the autoequivalence is "compatible", one can explicitly write down the action of this autoequivalence. In turn, the now understood autoequivalence can provide ways of extracting geometric information from the stability condition. In this thesis, we elaborate on what it means for an autoequivalence and stability condition to be "compatibile" and derive a sufficiency criterion.
Subject: Category theory Algebraic geometry Derived categories Moduli spaces Autoequivalences N-gons Stability conditions
URI: http://hdl.handle.net/2152/ETD-UT-2010-05-986
Date: 2010-05

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