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2017 On the Fano variety of linear spaces contained in two odd-dimensional quadrics
Carolina Araujo, Cinzia Casagrande
Geom. Topol. 21(5): 3009-3045 (2017). DOI: 10.2140/gt.2017.21.3009

Abstract

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 m1. 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).

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Carolina Araujo. Cinzia Casagrande. "On the Fano variety of linear spaces contained in two odd-dimensional quadrics." Geom. Topol. 21 (5) 3009 - 3045, 2017. https://doi.org/10.2140/gt.2017.21.3009

Information

Received: 14 February 2016; Revised: 29 July 2016; Accepted: 20 November 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 06774939
MathSciNet: MR3687113
Digital Object Identifier: 10.2140/gt.2017.21.3009

Subjects:
Primary: 14E30, 14J45
Secondary: 14E05, 14M15, 14N20

Rights: Copyright © 2017 Mathematical Sciences Publishers

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Vol.21 • No. 5 • 2017
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