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arXiv · 1809.03785

Kodaira vanishing for singular varieties revisited

Donu Arapura·Lei Song
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Abstract

We correct the proof and slightly strengthen a Kodaira-type vanishing theorem for singular varieties originally due to Jaffe and the first author. Specifically, we show that if $L$ is a nef and big line bundle on a projective variety of characteristic zero, the $i^{\text{th}}$ cohomology of $L^{-1}$ vanishes for $i$ in a range determined by the depth and dimension of the singular locus.

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Donu Arapura, Lei Song. 2018-09-11. Kodaira vanishing for singular varieties revisited. https://arxiv.org/abs/1809.03785

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