On $(2,4)$ complete intersection threefolds that contain an Enriques surface

Abstract

We study nodal complete intersection threefolds of type $(2,4)$ in $\PP^5$ which contain an Enriques surface in its Fano embedding. We completely determine Calabi-Yau birational models of a generic such threefold. These models have Hodge numbers $(h^{11},h^{12})=(2,32)$. We also describe Calabi-Yau varieties with Hodge numbers equal to $(2,26)$, $(23,5)$ and $(31,1)$. The last two pairs of Hodge numbers are, to the best of our knowledge, new.

30 pages, 1 figure. Added arguments so that most Macaulay calculations are not needed anymore

References in corpus (4)

• Derived categories of cubic fourfolds
• Hodge theory and derived categories of cubic fourfolds
• Lagrangian tens of planes, Enriques surfaces and holomorphic symplectic fourfolds
• Determinantal Quintics and Mirror Symmetry of Reye Congruences

Cited by in corpus (7)

• Calabi-Yau Threefolds With Small Hodge Numbers
• The movable cone of certain Calabi-Yau threefolds of Picard number two
• The movable cone of Calabi--Yau threefolds in ruled Fano manifolds
• A Strange Family of Calabi-Yau 3-folds
• Higher-dimensional Calabi-Yau varieties with dense sets of rational points
• Fano fourfolds with large anticanonical base locus
• On complete intersections with trivial canonical class