Abstract:Consider a family of Fano varieties π : X −→ B ∋ o over a curve germ with a smooth total space X. Assume that the generic fiber is smooth and the special fiber F = π −1 (o) has simple normal crossings. Then F is called a semistable degeneration of Fano varieties. We show that the dual complex of F is a simplex of dimension ≤ dim F . Simplices of any admissible dimension can be realized for any dimension of the fiber. Using this result and the Minimal Model Program in dimension 3 we reproduce the classification… Show more
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