Complete Calabi-Yau metrics in the complement of two divisors

TL;DR

This paper constructs new complete Calabi-Yau metrics on the complement of two divisors in Fano manifolds, using a generalized Calabi ansatz linked to non-archimedean Monge-Ampère equations, advancing geometric analysis in complex geometry.

Contribution

It introduces a novel method for constructing complete Calabi-Yau metrics in complex geometry involving two divisors, expanding understanding of asymptotic geometries.

Findings

Constructed new complete Calabi-Yau metrics on specific complex manifolds.

Linked asymptotic geometry to a generalized Calabi ansatz.

Connected geometric analysis with non-archimedean Monge-Ampère equations.

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.