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arXiv:math/0702539v3[math.AG]11Jul2008 The A Deformation Theory of a Point and the

Summary: arXiv:math/0702539v3[math.AG]11Jul2008
The A Deformation Theory of a Point and the
Derived Categories of Local Calabi-Yaus
Ed Segal
Department of Mathematics
Imperial College London, SW7 2AZ, UK
July 11, 2008
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.
1 Introduction 2
1.1 An example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5


Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield


Collections: Mathematics