Even nodal surfaces of K3 type

Marcello Bernardara; Enrico Fatighenti; Grzegorz Kapustka; Michał Kapustka; Laurent Manivel; Giovanni Mongardi; Fabio Tanturri

arXiv · 2402.08528

Even nodal surfaces of K3 type

Marcello Bernardara·Enrico Fatighenti·Grzegorz Kapustka·Michał Kapustka·Laurent Manivel·Giovanni Mongardi·Fabio Tanturri

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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.

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Marcello Bernardara, Enrico Fatighenti, Grzegorz Kapustka, Michał Kapustka, Laurent Manivel, Giovanni Mongardi, Fabio Tanturri. 2024-02-13. Even nodal surfaces of K3 type. https://arxiv.org/abs/2402.08528

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