On deformations of Fano threefolds with non-Gorenstein terminal singularities

Details On deformations of Fano threefolds with non-Gorenstein terminal singularities On deformations of Fano threefolds with non-Gorenstein terminal singularities

2012-03-28

arxiv.org/abs/1203.6323v2

Mathematics

Algebraic Geometry

23 pages. Corrected some mistakes in Section 4

Scientific paper

We study the deformation theory of Q-Fano 3-folds with only terminal singularities. First, we show that the Kuranishi spaces of Q-Fano 3-folds are smooth. Second, we show that Q-Fano 3-folds with only ordinary terminal singularities are Q-smoothable, that is, they can be deformed to Q-Fano 3-folds with only quotient singularities. Finally, we prove the existence of good deformations of pairs of Q-Fano 3-folds and their anticanonical elements with only isolated singularities. As an application, we get a genus bound for some primary Q-Fano 3-folds.

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