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arXiv · 1712.07967

Calabi-Yau metrics with conical singularities along line arrangements

Martin de Borbon·Cristiano Spotti
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Abstract

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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Martin de Borbon, Cristiano Spotti. 2017-12-21. Calabi-Yau metrics with conical singularities along line arrangements. https://arxiv.org/abs/1712.07967

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