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GENERAL HYPERPLANE SECTIONS OF THREEFOLDS IN POSITIVE CHARACTERISTIC

Published online by Cambridge University Press:  12 April 2018

Kenta Sato
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan (ktsato@ms.u-tokyo.ac.jp)
Shunsuke Takagi
Affiliation:
Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan (stakagi@ms.u-tokyo.ac.jp)
Corresponding

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 $H$.

Type
Research Article
Copyright
© Cambridge University Press 2018

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