Variations of mixed Hodge structure, Higgs fields, and quantum cohomology
Variations of mixed Hodge structure, Higgs fields, and quantum cohomology
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混合霍奇结构、希格斯场和量子上同调的变体
DOI：
10.1007/pl00005852
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发表时间：
1998
影响因子：
0.6
通讯作者：
G. Pearlstein
中科院分区：
文献类型：
--
作者：
G. Pearlstein
摘要：继 C. Simpson 之后，我们证明了在 ℚ 上定义的分级偏振混合 Hodge 结构的每个变体都带有自然的希格斯丛结构，该结构在[20]中研究的 ℂ* 作用下是不变的。然后，我们将我们的构造专门针对[6]的背景，并表明所得到的希格斯场 θ 决定了（并由其决定）卡拉比-丘三重基础族的格罗莫夫-威滕势。
Abstract: Following C. Simpson, we show that every variation of graded-polarized mixed Hodge structure defined over ℚ carries a natural Higgs bundle structure which is invariant under the ℂ* action studied in [20]. We then specialize our construction to the context of [6], and show that the resulting Higgs field θ determines (and is determined by) the Gromov–Witten potential of the underlying family of Calabi–Yau threefolds.