Asymptotics of complete Kähler metrics of finite volume on quasiprojective manifolds

Frédéric Rochon*, Zhou Zhang

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)

    Abstract

    Let X be a quasiprojective manifold given by the complement of a divisor D with normal crossings in a smooth projective manifold X. Using a natural compactification of X by a manifold with corners X~, we describe the full asymptotic behavior at infinity of certain complete Kähler metrics of finite volume on X. When these metrics evolve according to the Ricci flow, we prove that such asymptotic behaviors persist at later times by showing that the associated potential function is smooth up to the boundary on the compactification X~. However, when the divisor D is smooth with KX+[D]>0 so that the Ricci flow converges to a Kähler-Einstein metric, we show that this Kähler-Einstein metric has a rather different asymptotic behavior at infinity, since its associated potential function is polyhomogeneous with, in general, some logarithmic terms occurring in its expansion at the boundary.

    Original languageEnglish
    Pages (from-to)2892-2952
    Number of pages61
    JournalAdvances in Mathematics
    Volume231
    Issue number5
    DOIs
    Publication statusPublished - 2012

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