复杂化凯勒类的特殊代表

Selecta Mathematica Pub Date : 2024-07-01 DOI:10.1007/s00029-024-00955-1

Carlo Scarpa, Jacopo Stoppa

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摘要

受镜像对称中出现的构造的启发，我们研究了复杂化凯勒类的特殊代表，它们扩展了通常凯勒类的恒定标量曲率和极值代表的概念。特别是，我们提供了矩图解释，讨论了与紧凑化兰道-金兹堡模型的可能对应关系，并证明了这种特殊复杂化凯勒形式及其在某些环状情况下的大体积极限的存在性结果。

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Special representatives of complexified Kähler classes

Motivated by constructions appearing in mirror symmetry, we study special representatives of complexified Kähler classes, which extend the notions of constant scalar curvature and extremal representatives for usual Kähler classes. In particular, we provide a moment map interpretation, discuss a possible correspondence with compactified Landau–Ginzburg models, and prove existence results for such special complexified Kähler forms and their large volume limits in certain toric cases.

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Selecta Mathematica

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