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GENERAL HYPERPLANE SECTIONS OF THREEFOLDS IN POSITIVE CHARACTERISTIC

Part of: Surfaces and higher-dimensional varieties Local theory General commutative ring theory

Published online by Cambridge University Press:  12 April 2018

Kenta Sato  and
Shunsuke Takagi Open the ORCID record for Shunsuke Takagi [Opens in a new window]
Kenta Sato
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan ([email protected])
Shunsuke Takagi
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan ([email protected])
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Abstract

In this paper, we study the singularities of a general hyperplane section $H$ of a three-dimensional quasi-projective variety $X$ over an algebraically closed field of characteristic $p>0$. We prove that if $X$ has only canonical singularities, then $H$ has only rational double points. We also prove, under the assumption that $p>5$, that if $X$ has only klt singularities, then so does $H$.

Keywords

Bertini theoremcanonical singularitiesklt singularitiesMJ-canonical singularitiesstrongly F-regular singularities

MSC classification

Primary: 14B05: Singularities 14J17: Singularities 13A35: Characteristic $p$ methods (Frobenius endomorphism) and reduction to characteristic $p$; tight closure
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 19 , Issue 2 , March 2020 , pp. 647 - 661
Copyright
© Cambridge University Press 2018

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