| Description |
1 online resource (vii, 86 pages) : illustrations |
| Series |
Memoirs of the American Mathematical Society, 0065-9266 ; number 1011 |
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Memoirs of the American Mathematical Society ; no. 1011.
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| Contents |
Introduction -- Introduction to the dimer model -- Consistency -- Zig-zag flows and perfect matchings -- Toric algebras and algebraic consistency -- Geometric consistency implies algebraic consistency -- Calabi-Yau algebras from algebraically consistent dimers -- Non-commutative crepant resolutions |
| Summary |
"In this article we use techniques from algebraic geometry and homological algebra, together with ideas from string theory to construct a class of 3-dimensional Calabi-Yau algebras. The Calabi-Yau property appears throughout geometry and string theory and is increasingly being studied in algebra. We further show that the algebras constructed are examples of non-commutative crepant resolutions (NCCRs), in the sense of Van den Bergh, of Gorenstein affine toric threefolds. Dimer models, first studied in theoretical physics, give a way of writing down a class of non-commutative algebras, as the path algebra of a quiver with relations obtained from a 'superpotential'. Some examples are Calabi-Yau and some are not. We consider two types of 'consistency' conditions on dimer models, and show that a 'geometrically consistent' dimer model is 'algebraically consistent'. We prove that the algebras obtained from algebraically consistent dimer models are 3-dimensional Calabi-Yau algebras. This is the key step which allows us to prove that these algebras are NCCRs of the Gorenstein affine toric threefolds associated to the dimer models." |
| Notes |
"Volume 215, number 1011 (second of 5 numbers)." |
| Bibliography |
Includes bibliographical references (pages 85-86) and index |
| Notes |
English |
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Print version record |
| Subject |
Toric varieties.
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Calabi-Yau manifolds.
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Noncommutative algebras.
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Geometry, Algebraic.
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MATHEMATICS -- Geometry -- General.
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Calabi-Yau manifolds
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Geometry, Algebraic
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Noncommutative algebras
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Toric varieties
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Calabi-Yau-Mannigfaltigkeit
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Nichtkommutative Algebra
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Torische Varietät
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| Form |
Electronic book
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| ISBN |
9780821885147 |
|
0821885146 |
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