On K3 surfaces admitting symplectic automorphism of order 3

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, Morrison, and van Geemen and Sarti. In this talk, we will try to develop analogous results for K3 surfaces with symplectic automorphisms of order three: we will explicitly describe the induced action of these automorphisms on the K3-lattice, which is isometric to the second cohomology group of a K3 surface; we deduce the relation between the families that admitting these automorphisms and the ones given by their quotients. If time permits, we give some applications: one related to Shioda-Inose structures, and another one in the construction of infinite towers of isogeneous K3 surfaces. This is joint work with Alice Garbagnati.

algebraic geometry

Audience: researchers in the discipline

American Graduate Student Algebraic Geometry Seminar

Series comments: The American Graduate Student Algebraic Geometry Seminar (AGSAGS) is a virtual seminar by and for algebraic geometry graduate students.

The goal of this seminar is for graduate students to share their research through online talks and to provide an algebraic geometry graduate networking system. Grad students, postdocs, and professors are welcome to attend.

Seminars will be held on Mondays at 4 p.m. Eastern on Zoom. We hope this time is convenient for graduate students in the Americas, hence the name AGSAGS. Prior registration is required and interested participants should register here: sites.google.com/view/agsags/registration. In addition to graduate talks, there will be occasional social events.