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arXiv · 0812.3670

On the period map for prime Fano threefolds of degree 10

O. Debarre·A. Iliev·L. Manivel
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Abstract

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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O. Debarre, A. Iliev, L. Manivel. 2008-12-18. On the period map for prime Fano threefolds of degree 10. https://arxiv.org/abs/0812.3670

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