Even nodal surfaces of K3 type

TL;DR

This paper explores Fano fourfolds of K3 type with conic bundle structures, establishing links to hyperKähler varieties and describing families of nodal surfaces generalizing Kummer quartic surfaces.

Contribution

It introduces new geometric links between Fano fourfolds and hyperKähler varieties, and describes families of nodal surfaces as generalizations of Kummer quartic surfaces.

Findings

Families of nodal surfaces are described as generalizations of Kummer quartic surfaces.

Connections between Fano fourfolds and hyperKähler varieties are established.

Conic bundle structures relate different families via hyperbolic reduction.

Abstract

We study Fano fourfolds of K3 type with a conic bundle structure. We construct direct geometrical links between these fourfolds and hyperK\"ahler varieties. As a result we describe families of nodal surfaces that can be seen as generalisations of Kummer quartic surfaces. Each of these families actually arises through two families of Fano fourfolds, whose conic bundle structures are related by hyperbolic reduction.