Calabi–Yau metrics with conical singularities along line arrangements

Martin de Borbon; Cristiano Spotti

doi:10.4310/JDG/1680883576

Calabi–Yau metrics with conical singularities along line arrangements

Department of Mathematics

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Abstract

Given a finite collection of lines L_j ⊂ CP² together with real numbers 0 < β_j < 1 satisfying natural constraint conditions, we show the existence of a Ricci-flat Kähler metric g_RF with cone angle 2πβ_j along each line L_j asymptotic to a polyhedral Kähler cone at each multiple point. Moreover, we discuss a Chern-Weil formula that expresses the energy of g_RF as a logarithmic Euler characteristic with points weighted according to the volume density of the metric.

Original language	English
Journal	Journal of Differential Geometry
Volume	123
Issue	2
Pages (from-to)	195-239
Number of pages	45
ISSN	0022-040X
DOIs	https://doi.org/10.4310/JDG/1680883576
Publication status	Published - Feb 2023

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10.4310/JDG/1680883576

https://arxiv.org/pdf/1712.07967

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title = "Calabi–Yau metrics with conical singularities along line arrangements",

abstract = "Given a finite collection of lines Lj ⊂ CP2 together with real numbers 0 < βj < 1 satisfying natural constraint conditions, we show the existence of a Ricci-flat K{\"a}hler metric gRF with cone angle 2πβj along each line Lj asymptotic to a polyhedral K{\"a}hler cone at each multiple point. Moreover, we discuss a Chern-Weil formula that expresses the energy of gRF as a logarithmic Euler characteristic with points weighted according to the volume density of the metric.",

author = "{de Borbon}, Martin and Cristiano Spotti",

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AU - Spotti, Cristiano

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AB - Given a finite collection of lines Lj ⊂ CP2 together with real numbers 0 < βj < 1 satisfying natural constraint conditions, we show the existence of a Ricci-flat Kähler metric gRF with cone angle 2πβj along each line Lj asymptotic to a polyhedral Kähler cone at each multiple point. Moreover, we discuss a Chern-Weil formula that expresses the energy of gRF as a logarithmic Euler characteristic with points weighted according to the volume density of the metric.

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JO - Journal of Differential Geometry

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Calabi–Yau metrics with conical singularities along line arrangements

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