Kyoto Journal of Mathematics

Bundles of generalized theta functions over abelian surfaces

Dragos Oprea

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We study the Verlinde bundles of generalized theta functions constructed from moduli spaces of sheaves over abelian surfaces. In degree 0, the splitting type of these bundles is expressed in terms of indecomposable semihomogeneous factors. Furthermore, Fourier–Mukai symmetries of the Verlinde bundles are found consistently with strange duality. Along the way, a transformation formula for the theta bundles is derived, extending a theorem of Drézet–Narasimhan from curves to abelian surfaces.

Article information

Kyoto J. Math., Volume 59, Number 1 (2019), 125-166.

Received: 13 October 2016
Revised: 28 December 2016
Accepted: 28 December 2016
First available in Project Euclid: 20 October 2018

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Zentralblatt MATH identifier

Primary: 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli [See also 14D20, 14F05, 32Lxx]
Secondary: 14D20: Algebraic moduli problems, moduli of vector bundles {For analytic moduli problems, see 32G13} 14K99: None of the above, but in this section

moduli of sheaves Abelian surfaces generalized theta functions


Oprea, Dragos. Bundles of generalized theta functions over abelian surfaces. Kyoto J. Math. 59 (2019), no. 1, 125--166. doi:10.1215/21562261-2018-0004.

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