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Manifolds of low dimension with trivial canonical bundle in Grassmannians

Manifolds of low dimension with trivial canonical bundle in Grassmannians We study fourfolds with trivial canonical bundle which are zero loci of sections of homogeneous, completely reducible bundles over ordinary and classical complex Grassmannians. We prove that the only hyper-Kähler fourfolds among them are the example of Beauville and Donagi, and the example of Debarre and Voisin. In doing so, we give a complete classification of those varieties. We include also the analogous classification for surfaces and threefolds. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Manifolds of low dimension with trivial canonical bundle in Grassmannians

Benedetti, Vladimiro
Mathematische Zeitschrift , Volume 290 (2) – Jan 5, 2018
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References (20)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-017-2017-6
Publisher site
See Article on Publisher Site

Abstract

We study fourfolds with trivial canonical bundle which are zero loci of sections of homogeneous, completely reducible bundles over ordinary and classical complex Grassmannians. We prove that the only hyper-Kähler fourfolds among them are the example of Beauville and Donagi, and the example of Debarre and Voisin. In doing so, we give a complete classification of those varieties. We include also the analogous classification for surfaces and threefolds.

Journal

Mathematische Zeitschrift – Springer Journals

Published: Jan 5, 2018

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