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摘要
This paper studies the birational geometry of terminal Gorenstein Fano 3-folds. If Y is not -factorial, in most cases, it is possible to describe explicitly the divisor class group Cl Y by running a Minimal Model Program on X, a small -factorialization of Y. In this case, the generators of Cl Y/ Pic Y are "topological traces" of K-negative extremal contractions on X. One can show, as an application of these methods, that a number of families of non-factorial terminal Gorenstein Fano 3-folds are rational. In particular, I give some examples of rational quartic hypersurfaces with rk Cl Y = 2 and show that when rk Cl Y a parts per thousand yen 6, Y is always rational.
- 出版日期2012-9
