Nikulin orbifolds

Abstract: The theory of K3 surfaces with symplectic involutions and their quotients is now a well understood classical subject thanks to foundational works of Nikulin, and van Geemen and Sarti. In this talk we will try to develop an analogous theory in the context of hyperkahler fourfolds of K3${}^{[2]}$ type. First, we will present a latttice theoretic classification of such fourfolds which admit a symplectic involution. Then we will investigate the associated quotients that we call Nikulin orbifolds. These are orbifolds which admit a symplectic form on the smooth locus and hence are special cases of so called hyperkahler orbifolds. Finally, we shall discuss families of Nikulin orbifolds and their deformations called hyperkahler orbifolds of Nikulin type. As an application, we will provide a description of the first known example of a complete family of projective hyperkahler orbifolds. This is joint work with A. Garbagnati, C. Camere and G. Kapustka.

algebraic geometrycombinatorics

Audience: researchers in the topic

( slides | video )

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Online Nottingham algebraic geometry seminar

Series comments: Online geometry seminar, typically held on Thursday. This seminar takes place online via Microsoft Teams on the Nottingham University "Algebraic Geometry" team.

For recordings of past talks, copies of the speaker's slides, or to be added to the Team, please visit the seminar homepage at: kasprzyk.work/seminars/ag.html

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