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Severi varieties and their varieties of reductions

Identifieur interne : 000E62 ( Istex/Corpus ); précédent : 000E61; suivant : 000E63

Severi varieties and their varieties of reductions

Auteurs : A. Iliev ; L. Manivel

Source :

RBID : ISTEX:47488442F0824CAB35FA35136B437217F71E5C6C

English descriptors

Abstract

We study the varieties of reductions associated to the four Severi varieties, the first example of which is the Fano threefold of index 2 and degree 5 studied by Mukai and others. We prove that they are smooth but very special linear sections of Grassmann varieties, and rational Fano manifolds of dimension 3a and index a + 1, for a = 1, 2, 4, 8. We study their maximal linear spaces and prove that through the general point pass exactly three of them, a result we relate to Cartan’s triality principle. We also prove that they are compactifications of affine spaces.

Url:
DOI: 10.1515/crll.2005.2005.585.93

Links to Exploration step

ISTEX:47488442F0824CAB35FA35136B437217F71E5C6C

Le document en format XML

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<div type="abstract" xml:lang="en">We study the varieties of reductions associated to the four Severi varieties, the first example of which is the Fano threefold of index 2 and degree 5 studied by Mukai and others. We prove that they are smooth but very special linear sections of Grassmann varieties, and rational Fano manifolds of dimension 3a and index a + 1, for a = 1, 2, 4, 8. We study their maximal linear spaces and prove that through the general point pass exactly three of them, a result we relate to Cartan’s triality principle. We also prove that they are compactifications of affine spaces.</div>
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