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2020 Fano 4-folds with rational fibrations
Cinzia Casagrande
Algebra Number Theory 14(3): 787-813 (2020). DOI: 10.2140/ant.2020.14.787

Abstract

We study (smooth, complex) Fano 4-folds X having a rational contraction of fiber type, that is, a rational map X −−→Y that factors as a sequence of flips followed by a contraction of fiber type. The existence of such a map is equivalent to the existence of a nonzero, nonbig movable divisor on X. Our main result is that if Y is not 1 or 2, then the Picard number ρX of X is at most 18, with equality only if X is a product of surfaces. We also show that if a Fano 4-fold X has a dominant rational map X −−→Z, regular and proper on an open subset of X, with dim(Z)=3, then either X is a product of surfaces, or ρX is at most 12. These results are part of a program to study Fano 4-folds with large Picard number via birational geometry.

Citation

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Cinzia Casagrande. "Fano 4-folds with rational fibrations." Algebra Number Theory 14 (3) 787 - 813, 2020. https://doi.org/10.2140/ant.2020.14.787

Information

Received: 27 February 2019; Revised: 17 September 2019; Accepted: 8 November 2019; Published: 2020
First available in Project Euclid: 2 July 2020

MathSciNet: MR4113781
Digital Object Identifier: 10.2140/ant.2020.14.787

Subjects:
Primary: 14J45
Secondary: 14E30, 14J35

Rights: Copyright © 2020 Mathematical Sciences Publishers

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Vol.14 • No. 3 • 2020
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