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- W4301486572 abstract "We construct Q-factorial terminal Fano varieties, starting in dimension 4, whose nef cone jumps when the variety is deformed. It follows that de Fernex and Hacon's results on deformations of 3-dimensional Fanos are optimal. The examples are based on the existence of high-dimensional flips which deform to isomorphisms, generalizing the Mukai flop. We also extend de Fernex and Hacon's positive results on deformations of Fano varieties. Toric Fano varieties which are smooth in codimension 2 and Q-factorial in codimension 3 are rigid. The divisor class group is deformation-invariant for klt Fanos which are smooth in codimension 2 and Q-factorial in codimension 3. The Cox ring deforms in a flat family when a terminal Fano which is Q-factorial in codimension 3 is deformed. A side result which seems to be new is that the divisor class group of a klt Fano variety maps isomorphically to ordinary homology." @default.
- W4301486572 created "2022-10-05" @default.
- W4301486572 creator A5072058132 @default.
- W4301486572 date "2009-07-21" @default.
- W4301486572 modified "2023-10-18" @default.
- W4301486572 title "Jumping of the nef cone for Fano varieties" @default.
- W4301486572 doi "https://doi.org/10.48550/arxiv.0907.3617" @default.
- W4301486572 hasPublicationYear "2009" @default.
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