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- W4296581101 abstract "We study the birational geometry of a Fano 4-fold X from the point of view of Mori dream spaces; more precisely, we study rational contractions of X. Here a rational contraction is a rational map f: X-->Y, where Y is normal and projective, which factors as a finite sequence of flips, followed by a surjective morphism with connected fibers. Such f is called elementary if the difference of the Picard numbers of X and Y is 1. We first give a characterization of non-movable prime divisors in X, when X has Picard number at least 6; this is related to the study of birational and divisorial elementary rational contractions of X. Then we study the rational contractions of fiber type on X which are elementary or, more generally, quasi-elementary. The main result is that the Picard number of X is at most 11 if X has an elementary rational contraction of fiber type, and 18 if X has a quasi-elementary rational contraction of fiber type." @default.
- W4296581101 created "2022-09-22" @default.
- W4296581101 creator A5091615738 @default.
- W4296581101 date "2010-10-20" @default.
- W4296581101 modified "2023-09-29" @default.
- W4296581101 title "On the birational geometry of Fano 4-folds" @default.
- W4296581101 doi "https://doi.org/10.48550/arxiv.1010.4129" @default.
- W4296581101 hasPublicationYear "2010" @default.
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