沿线排列具有圆锥形奇点的Calabi–Yau度量

IF 1.3 1区数学 Q1 MATHEMATICS

Journal of Differential Geometry Pub Date : 2017-12-21 DOI:10.4310/jdg/1680883576

Martin de Borbon, Cristiano Spotti

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引用次数: 2

摘要

给定投影平面上的加权线排列，在权值满足自然约束条件的情况下，我们证明了一个Ricci-flat K\ ahler度规的存在性，该度规在每个多点上沿多面体K\ ahler圆锥渐近的直线上具有锥奇点。此外，我们讨论了一个chen - weil公式，该公式将度规的能量表示为根据度规的体积密度加权的点的“对数”欧拉特征。

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Calabi–Yau metrics with conical singularities along line arrangements

Given a weighted line arrangement in the projective plane, with weights satisfying natural constraint conditions, we show the existence of a Ricci-flat K\"ahler metric with cone singularities along the lines asymptotic to a polyhedral K\"ahler cone at each multiple point. Moreover, we discuss a Chern-Weil formula that expresses the energy of the metric as a `logarithmic' Euler characteristic with points weighted according to the volume density of the metric.

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来源期刊

Journal of Differential Geometry 数学-数学

CiteScore

3.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes the latest research in differential geometry and related areas of differential equations, mathematical physics, algebraic geometry, and geometric topology.