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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On Kodaira vanishing for singular varieties


Authors: Donu Arapura and David B. Jaffe
Journal: Proc. Amer. Math. Soc. 105 (1989), 911-916
MSC: Primary 14F15; Secondary 14F05, 32L20
DOI: https://doi.org/10.1090/S0002-9939-1989-0952313-8
MathSciNet review: 952313
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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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Keywords: Vanishing theorem, seminormal
Article copyright: © Copyright 1989 American Mathematical Society