Fano 4-folds, flips, and blow-ups of points

JOURNAL OF ALGEBRA

卷:483

Article

Casagrande, C.¹ 

[1] Univ Torino, Dipartimento Matemat, Via Carlo Alberto 10, I-10123 Turin, Italy

关键词: Fano 4-folds;    Birational geometry;    Picard number;   

DOI  :  10.1016/j.jalgebra.2017.03.027

来源: Elsevier

【 摘 要 】

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 <= 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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free