Hitchin and Calabi–Yau Integrable Systems via Variations of Hodge Structures
Hitchin and Calabi–Yau Integrable Systems via Variations of Hodge Structures
复制标题
希钦和卡拉比-丘可积系统（通过 Hodge 结构的变体）
DOI：
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复制
发表时间：
2017
影响因子：
0.7
通讯作者：
Florian Beck
中科院分区：
文献类型：
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作者：
Florian Beck
自1987年由Hitchin发现G-Hitchin系统以来，人们对G-Hitchin系统进行了广泛的研究。例如，现在人们对一般纤维已经很了解了。本文证明了简单伴随复李群G- hitchin系统的光滑部分与非紧Calabi-Yau可积系统同构，并由Diaconescu-Donagi-Pantev推广了结果。此外，我们还解释了Hitchin系统的Langlands对偶性与拟射影Calabi-Yau三倍的对应族的poincar<s:1> - verdier对偶性的关系。尽管这个命题是全纯辛的，但我们的证明是霍奇理论的。它是基于霍奇结构的极化变化，承认所谓的抽象塞伯格-威滕微分。这保证了相关雅可比颤振是一个代数可积系统。
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.
Calabi-Yau 可积和 Hitchin 系统的各个方面
DOI：
10.3842/sigma.2019.001
发表时间：
2019
期刊：
Symmetry, Integrability and Geometry: Methods and Applications
影响因子：
--
作者：
Florian Beck
通讯作者：
Florian Beck
希钦基地上空的 CalabiâYau 轨道折叠
影响因子：
1.5
作者：
Florian Beck
通讯作者：
Florian Beck