Steenbrink-type vanishing for surfaces in positive characteristic

IF 0.8 3区数学 Q2 MATHEMATICS Bulletin of the London Mathematical Society Pub Date : 2024-09-12 DOI:10.1112/blms.13146

Tatsuro Kawakami

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Abstract

Let $(X, B)$ be a pair of a normal surface over a perfect field of characteristic $p > 0$ and an effective $Q$ -divisor $B$ on $X$ . We prove that Steenbrink-type vanishing holds for $(X, B)$ if it is log canonical and $p > 5$ , or it is $F$ -pure. We also show that rational surface singularities satisfying the vanishing are $F$ -injective.

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正特征曲面的斯登布林克型消失

让 ( X , B ) $(X,B)$ 是一对在特性 p > 0 $p>0$ 的完全域上的法向面和在 X $X$ 上的有效 Q $\mathbb {Q}$ -divisor B $B$ 。我们证明，如果 ( X , B ) $(X,B)$ 是 log canonical 且 p > 5 $p>5$ 或它是 F $F$ 纯的，则 Steenbrink 型消失成立。我们还证明了满足消失的有理曲面奇点是 F $F$ -注入的。

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