论文标题
折叠希钦系统和毛茸茸的分辨率
Folding of Hitchin systems and crepant resolutions
论文作者
论文摘要
根据图自动形态的ADE-DYNKIN图的折叠产生了ABCDEFG型的不可还原的Dynkin图。此折叠过程允许将相应的简单Lie代数或组的属性追溯到ADE-Type的属性。在本文中，我们实施了Hitchin Antekable Systems通过图形自动形态折叠的技术。我们表明，这些自动形态的固定点基因座是同构成的同构，作为代数的集成系统，可远离单数纤维的折叠组的Hitchin系统。后一种Hitchin系统与第一作者构建的Calabi-Yayau Orbifold堆栈的中间雅各布纤维相同。我们同时构建了相关的奇异准主体calabi-yau三倍的近三倍的毛茸茸的分辨率，并将所得的中间雅各布纤维与相应的Hitchin Systems进行比较。
Folding of ADE-Dynkin diagrams according to graph automorphisms yields irreducible Dynkin diagrams of ABCDEFG-types. This folding procedure allows to trace back the properties of the corresponding simple Lie algebras or groups to those of ADE-type. In this article, we implement the techniques of folding by graph automorphisms for Hitchin integrable systems. We show that the fixed point loci of these automorphisms are isomorphic as algebraic integrable systems to the Hitchin systems of the folded groups away from singular fibers. The latter Hitchin systems are isomorphic to the intermediate Jacobian fibrations of Calabi--Yau orbifold stacks constructed by the first author. We construct simultaneous crepant resolutions of the associated singular quasi-projective Calabi--Yau threefolds and compare the resulting intermediate Jacobian fibrations to the corresponding Hitchin systems.
