Year: 2014
Type: preprint
Abstract: It is shown that a smooth global deformation of quartic double solids, i.e. double covers of $\mathbb P^3$ 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 $\mathbb P^ 5$ is also shown, which is, however, much easier. In a weak form this extends results of J. Kollár 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.
Source: arXiv (Cornell University)
Author: Dorsch, Tobias
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2096519632