Volume 21, issue 5 (2017)

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

Volume 26
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476

Volume 25, 7 issues

Volume 24, 7 issues

Volume 23, 7 issues

Volume 22, 7 issues

Volume 21, 6 issues

Volume 20, 6 issues

Volume 19, 6 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 4 issues

Volume 15, 4 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 4 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 3 issues

Volume 7, 2 issues

Volume 6, 2 issues

Volume 5, 2 issues

Volume 4, 1 issue

Volume 3, 1 issue

Volume 2, 1 issue

Volume 1, 1 issue

The Journal
About the Journal
Editorial Board
Editorial Interests
Editorial Procedure
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
On the Fano variety of linear spaces contained in two odd-dimensional quadrics

Carolina Araujo and Cinzia Casagrande

Geometry & Topology 21 (2017) 3009–3045

We describe the geometry of the 2m–dimensional Fano manifold G parametrizing (m1)–planes in a smooth complete intersection Z of two quadric hypersurfaces in the complex projective space 2m+2 for m 1. We show that there are exactly 22m+2 distinct isomorphisms in codimension one between G and the blow-up of 2m at 2m + 3 general points, parametrized by the 22m+2 distinct m–planes contained in Z, and describe these rational maps explicitly. We also describe the cones of nef, movable and effective divisors of G, as well as their dual cones of curves. Finally, we determine the automorphism group of G.

These results generalize to arbitrary even dimension the classical description of quartic del Pezzo surfaces (m = 1).

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 varieties, intersection of two quadrics, blow-up of projective spaces, birational geometry
Mathematical Subject Classification 2010
Primary: 14E30, 14J45
Secondary: 14M15, 14N20, 14E05
Received: 14 February 2016
Revised: 29 July 2016
Accepted: 20 November 2016
Published: 15 August 2017
Proposed: Lothar Göttsche
Seconded: Dan Abramovich, Gang Tian
Carolina Araujo
Instituto de Matemática Pura e Aplicada
22460-320 Rio de Janeiro
Cinzia Casagrande
Dipartimento di Matematica
Università di Torino
I-10123 Torino