Which quartic double solids are rational?

Abstract

We study the rationality problem for nodal quartic double solids. In particular, we prove that nodal quartic double solids with at most six singular points are irrational, and nodal quartic double solids with at least eleven singular points are rational.

35 pages

References in corpus (2)

• Unirational threefolds with no universal codimension 2 cycle
• A very general sextic double solid is not stably rational

Cited by in corpus (4)

• Fano threefolds with infinite automorphism groups
• Coble fourfold, $S_6$-invariant quartic threefolds, and Wiman-Edge sextics
• On the birational geometry of $\mathbf{Q}$-Fano threefolds of large Fano index, I
• On the birational geometry of sextic threefold hypersurface in $\mathbf{P}(1,1,2,2,3)$