Complete Calabi-Yau metrics in the complement of two divisors

Tristan C. Collins; Yang Li

Complete Calabi-Yau metrics in the complement of two divisors

Differential Geometry 2022-03-22 v1 Algebraic Geometry

Authors: Tristan C. Collins , Yang Li

Abstract

We construct new complete Calabi-Yau metrics on the complement of an anticanonical divisors $D$ in a Fano manifold of dimension at least three, when $D$ consists of two transversely intersecting smooth divisors. The asymptotic geometry is modeled on a generalization of the Calabi ansatz, related to the non-archimedean Monge-Amp\`ere equation.

Keywords

calabi-yau metrics fano manifold anticanonical divisors calabi ansatz monge-ampere equation

Cite

@article{arxiv.2203.10656,
  title  = {Complete Calabi-Yau metrics in the complement of two divisors},
  author = {Tristan C. Collins and Yang Li},
  journal= {arXiv preprint arXiv:2203.10656},
  year   = {2022}
}

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37 pages

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