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On Global Deformations of Quartic Double Solids
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On Global Deformations of Quartic Double Solids
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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. 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.
Forward citations
Cited by 2 Pith papers
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A connection between minimal nilpotent orbits of types A and D via Hamiltonian reduction
The affine closure of the cotangent bundle of the minimal nilpotent orbit O_n in sl_n is isomorphic to a C*-Hamiltonian reduction of the minimal nilpotent orbit closure in so_{2n+2}.
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A connection between minimal nilpotent orbits of types A and D via Hamiltonian reduction
Affine closure of T*O_n in sl_n is isomorphic via C*-Hamiltonian reduction to the minimal nilpotent orbit closure in so_{2n+2}, and has no symplectic resolution.
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