On the strange duality conjecture for abelian surfaces II
| Autor: | Kota Yoshioka, Dragos Oprea, Barbara Bolognese, Alina Marian |
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| Rok vydání: | 2016 |
| Předmět: |
Algebra and Number Theory
010102 general mathematics Duality (mathematics) Theta function Computer Science::Digital Libraries 01 natural sciences Representation theory Moduli space Moduli Combinatorics Mathematics::Algebraic Geometry 0103 physical sciences Computer Science::Mathematical Software 010307 mathematical physics Geometry and Topology Isomorphism 0101 mathematics Abelian group Arithmetic of abelian varieties Mathematics |
| Zdroj: | Journal of Algebraic Geometry. 26:475-511 |
| ISSN: | 1534-7486 1056-3911 |
| DOI: | 10.1090/jag/685 |
| Popis: | In the prequel to this paper, two versions of Le Potier’s strange duality conjecture for sheaves over abelian surfaces were studied. A third version is considered here. In the current setup, the isomorphism involves moduli spaces of sheaves with fixed determinant and fixed determinant of the Fourier-Mukai transform on one side, and moduli spaces where both determinants vary, on the other side. We first establish the isomorphism in rank 1 using the representation theory of Heisenberg groups. For product abelian surfaces, the isomorphism is then shown to hold for sheaves with fiber degree 1 1 via Fourier-Mukai techniques. By degeneration to product geometries, the duality is obtained generically for a large number of numerical types. Finally, it is shown in great generality that the Verlinde sheaves encoding the variation of the spaces of theta functions are locally free over moduli. |
| Databáze: | OpenAIRE |
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