Cohomological characterization of hyperquadrics of odd dimensions in characteristic two
Cohomological characterization of hyperquadrics of odd dimensions in characteristic two
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特征二奇维超二次曲面的上同调表征
DOI：
10.1007/s00209-014-1308-4
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发表时间：
2014
影响因子：
0.8
通讯作者：
Katsuhisa Furukawa
中科院分区：
文献类型：
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作者：
Katsuhisa Furukawa
我们考虑射影簇的特征在于他们的切线。Mori利用切丛的充实性建立了任意特征的射影空间的特征。Wahl通过切丛的上同调条件刻画了特征为零的射影空间;此外，他还指出，从奇维超二次型构造了特征为二的反例。这是由于二次曲面的每个嵌入切空间都包含一个公共点。一般来说，如果一个射影簇的嵌入切空间在中有这样一个公共点，则称它是奇异的。一条非线性光滑射影曲线是奇异的当且仅当它是特征二次曲线（Lluis，Samuel）。Kleiman和Piene证明了一个非线性光滑超曲面是奇异的当且仅当它是一个特征为2的奇维二次曲面。本文研究了完全交，证明了非线性光滑完全交是奇异的当且仅当它是特征二为奇维的二次曲面;这些条件也等价于切丛的-扭的-上同调不为零。
We consider characterizations of projective varieties in terms of their tangents. Mori established the characterization of projective spaces in arbitrary characteristic by ampleness of tangent bundles. Wahl characterized projective spaces in characteristic zero by cohomological condition of tangent bundles; in addition, he remarked that a counter-example in characteristic two is constructed from odd-dimensional hyperquadricswith. This is caused by existence of a common point inwhich every embedded tangent space to the quadric contains. In general, a projective variety inis said to be strange if its embedded tangent spaces admit such a common point in. A non-linear smooth projective curve is strange if and only if it is a conic in characteristic two (Lluis, Samuel). Kleiman and Piene showed that a non-linear smooth hypersurface inis strange if and only if it is a quadric of odd-dimension in characteristic two. In this paper, we investigate complete intersections, and prove that, a non-linear smooth complete intersection inis strange if and only if it is a quadric inof odd dimension in characteristic two; these conditions are also equivalent to non-vanishing of-cohomology of-twist of the tangent bundle.