Nilpotent orbits of a generalization of Hodge structures
Nilpotent orbits of a generalization of Hodge structures
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Hodge 结构推广的幂零轨道
DOI：
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发表时间：
2006
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通讯作者：
Christian Sevenheck
中科院分区：
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作者：
C. Hertling;Christian Sevenheck
摘要我们研究了最早出现在Cecotti和Vafa工作中的Hodge结构的一个推广。它由ℙ1上的全纯向量丛、ℂ*上的平坦联络、实子丛和配对组成。我们称这些对象为TERP结构。我们将Hodge结构的幂零轨道与极化混合Hodge结构的幂零轨道之间的Cattani、Kaplan和Schmid的对应推广到TERP-结构。这些证明使用了Simpson和Mochizuki关于涡旋结构的变化和极点在零和无穷远的Stokes结构的控制的工作。这些结果被应用于具有孤立奇点的全纯函数的振荡积分所产生的TERP结构。
Abstract We study a generalization of Hodge structures which first appeared in the work of Cecotti and Vafa. It consists of twistors, that is, holomorphic vector bundles on ℙ1, with additional structure, a flat connection on ℂ*, a real subbundle and a pairing. We call these objects TERP-structures. We generalize to TERP-structures a correspondence of Cattani, Kaplan and Schmid between nilpotent orbits of Hodge structures and polarized mixed Hodge structures. The proofs use work of Simpson and Mochizuki on variations of twistor structures and a control of the Stokes structures of the poles at zero and infinity. The results are applied to TERP-structures which arise via oscillating integrals from holomorphic functions with isolated singularities.