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

TL;DR

This paper investigates specific complete intersection threefolds containing Enriques surfaces, identifying their Calabi-Yau birational models and discovering new Hodge number configurations.

Contribution

It determines Calabi-Yau birational models for generic (2,4) complete intersection threefolds with Enriques surfaces and introduces new Hodge number pairs.

Findings

Calabi-Yau models with Hodge numbers (2,32), (2,26), (23,5), and (31,1) identified.

Complete classification of certain (2,4) threefolds containing Enriques surfaces.

New Hodge number pairs discovered for Calabi-Yau varieties.

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.