Calabi–Yau metrics with conical singularities along line arrangements

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, w...

Full description

Saved in:
Bibliographic Details
Main Authors: Martin de Borbon, Cristiano Spotti
Format: Default Article
Published: 2023
Subjects:
Pure mathematics
General Mathematics
Online Access:https://hdl.handle.net/2134/24526213.v1
Tags: Add Tag
No Tags, Be the first to tag this record!
_version_ 1818165143033348096
author Martin de Borbon
Cristiano Spotti
author_facet Martin de Borbon
Cristiano Spotti
author_sort Martin de Borbon (16976562)
collection Figshare
description 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.
format Default
Article
id rr-article-24526213
institution Loughborough University
publishDate 2023
record_format Figshare
spelling rr-article-245262132023-02-01T00:00:00Z Calabi–Yau metrics with conical singularities along line arrangements Martin de Borbon (16976562) Cristiano Spotti (17361656) Pure mathematics General Mathematics <p>Given a finite collection of lines L<sub>j</sub> ⊂ CP<sup>2</sup> 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 2πβ<sub>j</sub> along each line L<sub>j</sub> 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.</p> 2023-02-01T00:00:00Z Text Journal contribution 2134/24526213.v1 https://figshare.com/articles/journal_contribution/Calabi_Yau_metrics_with_conical_singularities_along_line_arrangements/24526213 CC BY-NC-ND 4.0
spellingShingle Pure mathematics
General Mathematics
Martin de Borbon
Cristiano Spotti
Calabi–Yau metrics with conical singularities along line arrangements
title Calabi–Yau metrics with conical singularities along line arrangements
title_full Calabi–Yau metrics with conical singularities along line arrangements
title_fullStr Calabi–Yau metrics with conical singularities along line arrangements
title_full_unstemmed Calabi–Yau metrics with conical singularities along line arrangements
title_short Calabi–Yau metrics with conical singularities along line arrangements
title_sort calabi–yau metrics with conical singularities along line arrangements
topic Pure mathematics
General Mathematics
url https://hdl.handle.net/2134/24526213.v1

Similar Items