Vanishing and Semipositivity Theorems for Semi-log Canonical Pairs

  • Osamu Fujino

    Osaka University, Japan
Vanishing and Semipositivity Theorems for Semi-log Canonical Pairs cover

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Abstract

We prove an effective vanishing theorem for direct images of log pluricanonical bundles of projective semi-log canonical pairs. As an application, we obtain a semipositivity theorem for direct images of relative log pluricanonical bundles of projective semi-log canonical pairs over curves, which implies the projectivity of the moduli spaces of stable varieties. It is worth mentioning that we do not use the theory of variation of (mixed) Hodge structure.

Cite this article

Osamu Fujino, Vanishing and Semipositivity Theorems for Semi-log Canonical Pairs. Publ. Res. Inst. Math. Sci. 56 (2020), no. 1, pp. 15–32

DOI 10.4171/PRIMS/56-1-2