JournalsjemsVol. 11, No. 4pp. 755–776

Limits of Calabi–Yau metrics when the Kähler class degenerates

  • Valentino Tosatti

    Harvard University, Cambridge, United States
Limits of Calabi–Yau metrics when the Kähler class degenerates cover
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Abstract

We study the behavior of families of Ricci-flat Kähler metrics on a projective Calabi– Yau manifold when the Kähler classes degenerate to the boundary of the ample cone. We prove that if the limit class is big and nef the Ricci-flat metrics converge smoothly on compact sets outside a subvariety to a limit incomplete Ricci-flat metric. The limit can also be understood from algebraic geometry.

Cite this article

Valentino Tosatti, Limits of Calabi–Yau metrics when the Kähler class degenerates. J. Eur. Math. Soc. 11 (2009), no. 4, pp. 755–776

DOI 10.4171/JEMS/165