On the period map for prime Fano threefolds of degree 10

Details On the period map for prime Fano threefolds of degree 10 On the period map for prime Fano threefolds of degree 10

2008-12-18

arxiv.org/abs/0812.3670v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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