Bott vanishing for Fano threefolds

IF 1 3区数学 Q1 MATHEMATICS

Mathematische Zeitschrift Pub Date : 2024-04-20 DOI:10.1007/s00209-024-03468-x

Burt Totaro

引用次数: 0

Abstract

Bott proved a strong vanishing theorem for sheaf cohomology on projective space, namely that \(H^j(X,\Omega ^i_X\otimes L)=0\) for \(j>0\), \(i\ge 0\), and L ample. This holds for toric varieties, but not for most other varieties. We classify the smooth Fano threefolds that satisfy Bott vanishing. There are many more than expected.

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法诺三折的底消失

博特证明了投影空间上的剪子同调的强消失定理，即对于 \(j>0\), \(i\ge 0\), 和 L ample，\(H^j(X,\Omega ^i_X\otimes L)=0\) 。这对环状变种成立，但对大多数其他变种不成立。我们对满足底消失的光滑法诺三褶进行了分类。比预想的要多得多。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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