General hyperplane sections of threefolds in positive characteristic

2017/03/02 by Sato, Kenta, Takagi, Shunsuke · 1 citation
#13A35 #14B05 #14J17 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.00770

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.

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• Boundedness of complements for fibered Fano threefolds in positive characteristic

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