Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerations
Period integrals from wall structures via tropical cycles, canonical coordinates in mirror symmetry and analyticity of toric degenerations
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墙体结构通过热带周期的周期积分、镜像对称的正则坐标和环面退化的分析性
DOI：
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Bernd S Siebert
中科院分区：
文献类型：
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作者：
Helge Ruddat;Bernd S Siebert
我们给出了由壁结构和中心纤维环面簇的联合构成的簇的退化家族中规范全纯体积形式的积分的简单表达式。要积分的循环是由中心纤维交叉复合体中的热带 1 循环构建的。一项应用证明格罗斯和第二作者构建的 Calabi-Yau 品种规范正式家族的镜像图是微不足道的。我们还表明，这些族是解析族的完成，无需重新参数化，并且它们在形式上与对数格式的变形是通用的。其他应用包括具有指定 Picard 群的 K3 表面的规范单参数 III 型简并。作为独立兴趣的技术成果，我们开发了一种关于法向交叉解析空间的有限阶变形的具有对数极点的周期积分理论。
We give a simple expression for the integral of the canonical holomorphic volume form in degenerating families of varieties constructed from wall structures and with central fiber a union of toric varieties. The cycles to integrate over are constructed from tropical 1-cycles in the intersection complex of the central fiber. One application is a proof that the mirror map for the canonical formal families of Calabi-Yau varieties constructed by Gross and the second author is trivial. We also show that these families are the completion of an analytic family, without reparametrization, and that they are formally versal as deformations of logarithmic schemes. Other applications include canonical one-parameter type III degenerations of K3 surfaces with prescribed Picard groups. As a technical result of independent interest we develop a theory of period integrals with logarithmic poles on finite order deformations of normal crossing analytic spaces.
环面变体放大的拉格朗日纤维和超曲面的镜面对称
DOI：
10.1007/s10240-016-0081-9
发表时间：
2016
期刊：
Publications mathématiques de l'IHÉS
影响因子：
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作者：
Abouzaid, Mohammed;Auroux, Denis;Katzarkov, Ludmil
通讯作者：
Katzarkov, Ludmil