Translator Disclaimer
August 2019 Further Evaluation of Wahl Vanishing Theorems for Surface Singularities in Characteristic p
Masayuki Hirokado
Michigan Math. J. 68(3): 621-636 (August 2019). DOI: 10.1307/mmj/1560391418

Abstract

Let (SpecR,m) be a rational double point defined over an algebraically closed field k of characteristic p0. We evaluate further the dimensions of the local cohomology groups, which were treated by Wahl in 1975 as vanishing theorem C (resp., D) under the assumption that p is a very good prime (resp., good prime) with respect to (SpecR,m). We use Artin’s classification of rational double points and completely determine the dimensions dimkHE1(SX) and dimkHE1(SXOX(E)), supplementing Wahl’s theorems. In the proof, we concretely construct derivations that do not lift to the minimal resolution XSpecR and an equisingular family that injects into a versal deformation of the rational double point (SpecR,m).

Citation

Download Citation

Masayuki Hirokado. "Further Evaluation of Wahl Vanishing Theorems for Surface Singularities in Characteristic p." Michigan Math. J. 68 (3) 621 - 636, August 2019. https://doi.org/10.1307/mmj/1560391418

Information

Received: 9 October 2017; Revised: 17 June 2018; Published: August 2019
First available in Project Euclid: 13 June 2019

zbMATH: 07130701
MathSciNet: MR3990173
Digital Object Identifier: 10.1307/mmj/1560391418

Subjects:
Primary: 14B05, 14G17
Secondary: 14B07, 14J17

Rights: Copyright © 2019 The University of Michigan

JOURNAL ARTICLE
16 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.68 • No. 3 • August 2019
Back to Top