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Summary: The A Deformation Theory of a Point
and the Derived Categories of Local
Calabi-Yaus
Edward Paul Segal
Imperial College London
Department of Mathematics
Thesis presented for the degree of
Doctor of Philosophy
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Abstract
Let A be an augmented algebra over a semi-simple algebra S. We
show that the Ext algebra of S as an A-module, enriched with its natural
A-infinity structure, can be used to reconstruct the completion of A at the
augmentation ideal. We use this technical result to justify a calculation
in the physics literature describing algebras that are derived equivalent
to certain non-compact Calabi-Yau three-folds. Since the calculation pro-
duces superpotentials for these algebras we also include some discussion
of superpotential algebras and their invariants.
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