Duke Mathematical Journal
- Duke Math. J.
- Volume 165, Number 15 (2016), 2991-3042.
Partial Fourier–Mukai transform for integrable systems with applications to Hitchin fibration
Let be an abelian scheme over a scheme . The Fourier–Mukai transform gives an equivalence between the derived category of and the derived category of the dual abelian scheme. We partially extend this to certain schemes over (which we call degenerate abelian schemes) whose generic fiber is an abelian variety, while special fibers are singular.
Our main result provides a fully faithful functor from a twist of the derived category of to the derived category of . Here is the algebraic space classifying fiberwise numerically trivial line bundles.
Next, we show that every algebraically integrable system gives rise to a degenerate abelian scheme and discuss applications to Hitchin systems.
Duke Math. J., Volume 165, Number 15 (2016), 2991-3042.
Received: 10 November 2014
Revised: 19 October 2015
First available in Project Euclid: 16 August 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 14D24: Geometric Langlands program: algebro-geometric aspects [See also 22E57]
Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20] 14K30: Picard schemes, higher Jacobians [See also 14H40, 32G20] 14L15: Group schemes
Arinkin, Dima; Fedorov, Roman. Partial Fourier–Mukai transform for integrable systems with applications to Hitchin fibration. Duke Math. J. 165 (2016), no. 15, 2991--3042. doi:10.1215/00127094-3645223. https://projecteuclid.org/euclid.dmj/1471368610