Families of Calabi-Yau manifolds and canonical singularities

Valentino Tosatti*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Given a polarized family of varieties over Δ, smooth over Δ×and with smooth fibers Abstract, Calabi-Yau, we show that the origin lies at finite Weil-Petersson distance if and only if after a finite base change the family is birational to one with central fiber a Calabi-Yau variety with at worst canonical singularities, answering a question of C.-L. Wang. This condition also implies that the Ricci-flat Kähler metrics in the polarization class on the smooth fibers have uniformly bounded diameter, or are uniformly volume non-collapsed.

Original languageEnglish (US)
Pages (from-to)10586-10594
Number of pages9
JournalInternational Mathematics Research Notices
Volume2015
Issue number20
DOIs
StatePublished - 2015

ASJC Scopus subject areas

  • Mathematics(all)

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