Moduli spaces of stable objects in Enriques categories
Alexander Perry, Laura Pertusi, and Xiaolei Zhao
TL;DR
This paper investigates the structure of moduli spaces of stable objects in Enriques categories, linking them to K3 categories, and proves nonemptiness results for these moduli spaces in various geometric contexts.
Contribution
It establishes the nonemptiness of moduli spaces of stable objects in Enriques categories and related hyperkähler varieties, expanding understanding of their geometric properties.
Findings
Nonemptiness of moduli spaces in Enriques categories
Nonemptiness of fixed loci of antisymplectic involutions
Connections between Enriques and K3 categories
Abstract
We study moduli spaces of stable objects in Enriques categories by exploiting their relation to moduli spaces of stable objects in associated K3 categories. In particular, we settle the nonemptiness problem for moduli spaces of stable objects in the Kuznetsov components of several interesting classes of Fano varieties, and deduce the nonemptiness of fixed loci of certain antisymplectic involutions on modular hyperk\"{a}hler varieties.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Nonlinear Waves and Solitons