Courbes elliptiques sur la variete spinorielle

Details Courbes elliptiques sur la variete spinorielle Courbes elliptiques sur la variete spinorielle

2006-07-11

arxiv.org/abs/math/0607260v1

Mathematics

Algebraic Geometry

12 pages in french, 1 figure. This a generalisation to higher dimension of the results of the paper math.AG/0409125

Scientific paper

Let V be an even dimensional vector space with a non degenerate quadratic form. We denote by X the variety of maximal isotropic subspaces in V (in fact one of its two connected components). In this paper, we prove the irreducibility of the scheme of degree d morphism f:C->X as soon as d is bigger than 1/2dim(V)-1. When dim(V)=10 and d=6, this result was used by A. Iliev and D. Markushevich in math.AG/0403122 to prove the irreducibility of the moduli space M_{X_12}(2,1,6) where X_{12} is the Fano threefold of index 1 and degree 12.

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