Simple isotropic decompositions of the curve sections of the known Enriques-Fano threefolds

TL;DR

This paper analyzes the curve sections of known Enriques-Fano threefolds using simple isotropic decompositions, helping to classify the moduli space of polarized Enriques surfaces and their associated families.

Contribution

It introduces a method to decompose curve sections isotropically, linking hyperplane sections of Enriques-Fano threefolds to specific families of polarized Enriques surfaces.

Findings

Identification of irreducible components of the moduli space

Classification of hyperplane sections within families of polarized Enriques surfaces

Enhanced understanding of the structure of Enriques-Fano threefolds

Abstract

In this paper, we describe the simple isotropic decompositions of the curve sections of the known Enriques-Fano threefolds. The simple isotropic decompositions allow us to identify the irreducible components of the moduli space of the polarized Enriques surfaces. Thus, our analysis will enable us to show to which families of polarized Enriques surfaces the hyperplane sections of the Enriques-Fano threefolds belong.