On the period map for prime Fano threefolds of degree 10 - Archive ouverte HAL Accéder directement au contenu
Article Dans Une Revue Journal of Algebraic Geometry Année : 2012

On the period map for prime Fano threefolds of degree 10

Laurent Manivel

Résumé

We prove that the deformations of a smooth complex Fano threefold X with Picard number 1, index 1, and degree 10, are unobstructed. The differential of the period map has two-dimensional kernel. We construct two two-dimensional components of the fiber of the period map through X: one is isomorphic to the variety of conics in X, modulo an involution, another is birationally isomorphic to a moduli space of semistable rank-2 torsion-free sheaves on X, modulo an involution. The threefolds corresponding to points of these components are obtained from X via conic and line (birational) transformations.

Dates et versions

hal-01250906 , version 1 (05-01-2016)

Identifiants

Citer

Laurent Manivel. On the period map for prime Fano threefolds of degree 10. Journal of Algebraic Geometry, 2012, 21 (1), pp.21-59. ⟨10.1090/S1056-3911-2011-00594-8⟩. ⟨hal-01250906⟩
24 Consultations
0 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More