A classification of terminal quartic 3-folds and applications to rationality questions
Algebraic Geometry
2009-08-04 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0908.0289,
title = {A classification of terminal quartic 3-folds and applications to rationality questions},
author = {Anne-Sophie Kaloghiros},
journal= {arXiv preprint arXiv:0908.0289},
year = {2009}
}
Comments
40 pages