Matrix factorizations in higher codimension
| Autor: | Jesse Burke, Mark E. Walker |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Discrete mathematics
Ring (mathematics) Pure mathematics Mathematics::Commutative Algebra Homotopy category Applied Mathematics General Mathematics Complete intersection Codimension Commutative Algebra (math.AC) Mathematics - Commutative Algebra Complete intersection ring Cohomology Mathematics - Algebraic Geometry Hypersurface FOS: Mathematics Algebraic Geometry (math.AG) Resolution (algebra) Mathematics |
| Zdroj: | Transactions of the American Mathematical Society. 367:3323-3370 |
| ISSN: | 1088-6850 0002-9947 |
| Popis: | We observe that there is an equivalence between the singularity category of an affine complete intersection and the homotopy category of matrix factorizations over a related scheme. This relies in part on a theorem of Orlov. Using this equivalence, we give a geometric construction of the ring of cohomology operators, and a generalization of the theory of support varieties, which we call stable support sets. We settle a question of Avramov about which stable support sets can arise for a given complete intersection ring. We also use the equivalence to construct a projective resolution of a module over a complete intersection ring from a matrix factorization, generalizing the well-known result in the hypersurface case. 41 pages |
| Databáze: | OpenAIRE |
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