Fano 4-folds with b2 > 12 are products of surfaces

• 成果类型: Article
• 署名作者: Casagrande, C.
• 署名单位: University of Turin
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-024-01236-6
• 发表日期: 2024
• 页码: 1-16
• 关键词: contractions; divisors

摘要

Let X be a smooth, complex Fano 4-fold, and rho(X) its Picard number. We show that if rho(X) > 12, then X is a product of del Pezzo surfaces. The proof relies on a careful study of divisorial elementary contractions f : X -> Y such that dim f (Exc(f)) = 2, together with the author's previous work on Fano 4-folds. In particular, given f : X -> Y as above, under suitable assumptions we show that S := f(Exc(f)) is a smooth del Pezzo surface with -K-S = (-K-Y)(|S).