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Complete Calabi-Yau metrics in the complement of two divisors

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arxiv 2203.10656 v1 pith:ZXECLU2B submitted 2022-03-20 math.DG math.AG

Tristan C. Collins , Yang Li This is my paper · ORCID
classification math.DGmath.AG
keywords divisorscalabi-yaucomplementcompletemetricsansatzanticanonicalasymptotic
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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.

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  1. On a general class of free boundary Monge-Amp\`ere equations

    math.AP 2025-08 conditional novelty 8.0 of 10

    A general existence theorem for free-boundary Monge-Ampere equations with prescribed gradient image, applied to degenerate optimal transport, Monge-Ampere eigenvalues, a hemispherical Minkowski problem, and free-bound...

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