On Kodaira vanishing for singular varieties

Arapura, Donu; Jaffe, David B.

doi:10.1090/S0002-9939-1989-0952313-8

On Kodaira vanishing for singular varieties
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by Donu Arapura and David B. Jaffe PDF

Proc. Amer. Math. Soc. 105 (1989), 911-916 Request permission

Abstract:

If $X$ is a complex projective variety with an ample line bundle $L$, we show that ${H^i}(X,{L^{ - 1}}) = 0$ for any $i{\text { < codim[Sing(}}X{\text {)]}}$, provided that $X$ satisfies Serre’s condition ${S_{i + 1}}$. We also give examples to show that these results are sharp. Finally, we prove a vanishing theorem (for ${H^1}$) for seminormal varieties

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