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Induced Automorphisms on Irreducible Symplectic Manifolds

2014/05/31 by Giovanni Mongardi, Malte Wandel
Mathematics · #math.AG #msc:14D06 #msc:14F05 #msc:14J50 #msc:14K30

paper · pdf · doi:10.1112/jlms/jdv012

22 pages; 2nd version: the part on automorphisms of O'Grady's manifolds acting trivially on cohomology has been removed and is now part of arXiv:1411.0759

arxiv created 2014/11/19 · arxiv updated 2015/06/12

Abstract

We introduce the notion of induced automorphisms in order to state a criterion to determine whether a given automorphism on a manifold of K3[n] type is, in fact, induced by an automorphism of a K3 surface and the manifold is a moduli space of stable objects on the K3. This criterion is applied to the classification of non-symplectic prime order automorphisms on manifolds of K3[2] type and we prove that almost all cases are covered. Variations of this notion and the above criterion are introduced and discussed for the other known deformation types of irreducible symplectic manifolds. Furthermore we provide a description of the Picard lattice of several irreducible symplectic manifolds having a lagrangian fibration.

Citations