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On Global Deformations of Quartic Double Solids

Tobias Dorsch

Number 11
Author Tobias Dorsch
Year 2014

It is shown that a smooth global deformation of quartic double solids, i.e. double covers of P3 branched along smooth quartics, is again a quartic double solid without assuming the projectivity of the global deformation. The analogous result for smooth intersections of two quadrics in P5 is also shown, which is, however, much easier.
In a weak form this extends results of J. Koll\'ar and I. Nakamura on Moishezon manifolds that are homeomorphic to certain Fano threefolds and it gives some further evidence for the question whether global deformations of Fano manifolds of Picard rank 1 are Fano themselves.

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