Vol. 14, No. 3, 2020

Download this article
Download this article For screen
For printing
Recent Issues

Volume 15
Issue 5, 1077–1342
Issue 4, 821–1076
Issue 3, 569–820
Issue 2, 309–567
Issue 1, 1–308

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Fano 4-folds with rational fibrations

Cinzia Casagrande

Vol. 14 (2020), No. 3, 787–813

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.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

Fano 4-folds, Mori dream spaces, birational geometry, MMP
Mathematical Subject Classification 2010
Primary: 14J45
Secondary: 14E30, 14J35
Received: 27 February 2019
Revised: 17 September 2019
Accepted: 8 November 2019
Published: 1 June 2020
Cinzia Casagrande
Dipartimento di Matematica
Università di Torino