Deforming elephants of Q-Fano threefolds

2014/04/03 by Sano, Taro
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1404.0909

Abstract

We study deformations of a pair of a ℚ-Fano 3-fold X with only terminal singularities and its elephant D ∈ |-K_X|. We prove that, if there exists D ∈ |-K_X| with only isolated singularities, the pair (X,D) can be deformed to a pair of a ℚ-Fano 3-fold with only quotient singularities and a Du Val elephant. When there are only non-normal elephants, we reduce the existence problem of such a deformation to a local problem around the singular locus of the elephant. We also give several examples of ℚ-Fano 3-folds without Du Val elephants.

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• Deformations of weak Fano 3-folds with only terminal singularities