2009/08/03 by Anne-Sophie Kaloghiros, Kaloghiros, Anne-Sophie
Mathematics · #14E30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.0908.0289
openalex publication_date 2009/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the birational geometry of terminal Gorenstein Fano 3-folds. If Y is not Q-factorial, in most cases, it is possible to describe explicitly the divisor class group Cl Y by running a Minimal Model Program (MMP) on X, a small Q-factorialisation of Y. In this case, Weil non-Cartier divisors are generated by "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 Cl Y of rank 2, and show that when Cl Y has rank greater than 6, Y is always rational.