Hitchin and Calabi–Yau integrable systems via variations of Hodge structures. (24th November 2020)
- Record Type:
- Journal Article
- Title:
- Hitchin and Calabi–Yau integrable systems via variations of Hodge structures. (24th November 2020)
- Main Title:
- Hitchin and Calabi–Yau integrable systems via variations of Hodge structures
- Authors:
- Beck, Florian
- Abstract:
- Abstract: Since its discovery by Hitchin in 1987, G -Hitchin systems for a reductive complex Lie group G have extensively been studied. For example, the generic fibers are nowadays well-understood. In this paper, we show that the smooth parts of G -Hitchin systems for a simple adjoint complex Lie group G are isomorphic to non-compact Calabi–Yau integrable systems extending results by Diaconescu–Donagi–Pantev. Moreover, we explain how Langlands duality for Hitchin systems is related to Poincaré–Verdier duality of the corresponding families of quasi-projective Calabi–Yau threefolds. Even though the statement is holomorphic-symplectic, our proof is Hodge-theoretic. It is based on polarizable variations of Hodge structures that admit so-called abstract Seiberg–Witten differentials. These ensure that the associated Jacobian fibration is an algebraic integrable system.
- Is Part Of:
- Quarterly journal of mathematics. Volume 71:Part 4(2020)
- Journal:
- Quarterly journal of mathematics
- Issue:
- Volume 71:Part 4(2020)
- Issue Display:
- Volume 71, Issue 4, Part 4 (2020)
- Year:
- 2020
- Volume:
- 71
- Issue:
- 4
- Part:
- 4
- Issue Sort Value:
- 2020-0071-0004-0004
- Page Start:
- 1345
- Page End:
- 1375
- Publication Date:
- 2020-11-24
- Subjects:
- Mathematics -- Periodicals
510 - Journal URLs:
- http://qjmath.oxfordjournals.org/ ↗
http://www3.oup.co.uk/qmathj/ ↗
http://ukcatalogue.oup.com/ ↗ - DOI:
- 10.1093/qmath/haaa037 ↗
- Languages:
- English
- ISSNs:
- 0033-5606
- Deposit Type:
- Legaldeposit
- View Content:
- Available online (eLD content is only available in our Reading Rooms) ↗
- Physical Locations:
- British Library DSC - 7192.000000
British Library DSC - BLDSS-3PM
British Library HMNTS - ELD Digital store - Ingest File:
- 15238.xml