# 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.