Non-commutative Desingularization of Determinantal Varieties, II: Arbitrary Minors
| Autor: | Michel Van den Bergh, Ragnar-Olaf Buchweitz, Graham J. Leuschke |
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| Přispěvatelé: | Algebra, Mathematics |
| Jazyk: | angličtina |
| Rok vydání: | 2016 |
| Předmět: |
Mathematical sciences
Operations research Mathematics::Commutative Algebra business.industry General Mathematics 010102 general mathematics Library science Foundation (evidence) 16. Peace & justice United States National Security Agency Mathematics - Commutative Algebra Commutative Algebra (math.AC) 01 natural sciences Mathematics - Algebraic Geometry Hospitality 0103 physical sciences FOS: Mathematics 14A22 13C14 14M12 16S38 14E15 14M15 15A75 010307 mathematical physics 0101 mathematics business Commutative property Algebraic Geometry (math.AG) Mathematics |
| Zdroj: | Vrije Universiteit Brussel |
| Popis: | In our paper "Non-commutative desingularization of determinantal varieties, I" we constructed and studied non-commutative resolutions of determinantal varieties defined by maximal minors. At the end of the introduction we asserted that the results could be generalized to determinantal varieties defined by non-maximal minors, at least in characteristic zero. In this paper we prove the existence of non-commutative resolutions in the general case in a manner which is still characteristic free, and carry out the explicit description by generators and relations in characteristic zero. As an application of our results we prove that there is a fully faithful embedding between the bounded derived categories of the two canonical (commutative) resolutions of a determinantal variety, confirming a well-known conjecture of Bondal and Orlov in this special case. Comment: 61 pages, greatly expanded. Now includes a complete treatment of the case of characteristic zero. All comments welcome |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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