Fano 4-folds, flips, and blow-ups of points
Algebraic Geometry
2017-04-06 v2
Abstract
In this paper we study smooth, complex Fano 4-folds X with large Picard number rho(X), with techniques from birational geometry. Our main result is that if X is isomorphic in codimension one to the blow-up of a smooth projective 4-fold Y at a point, then rho(X) is at most 12. We give examples of such X with Picard number up to 9. The main theme (and tool) is the study of fixed prime divisors in Fano 4-folds, especially in the case rho(X)>6, in which we give some general results of independent interest.
Keywords
Cite
@article{arxiv.1511.01738,
title = {Fano 4-folds, flips, and blow-ups of points},
author = {Cinzia Casagrande},
journal= {arXiv preprint arXiv:1511.01738},
year = {2017}
}
Comments
44 pages. Minor changes, to appear in the Journal of Algebra