Induced Automorphisms on Irreducible Symplectic Manifolds

Abstract

We introduce the notion of induced automorphisms in order to state a criterion to determine whether a given automorphism on a manifold of $K{3}^{[n]}$ 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 $K{3}^{[2]}$ 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.

arXiv comment22 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

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Cited by in corpus (10)

• Hyperkähler fourfolds and Kummer surfaces
• On the monodromy group of desingularised moduli spaces of sheaves on K3 surfaces
• Non-symplectic involutions of irreducible symplectic manifolds of K3^[n]-type
• Induced birational transformations on O'Grady's sixfolds
• Non-symplectic automorphisms of odd prime order on manifolds of $K{3}^{[n]}$-type
• Sixfolds of generalized Kummer type and K3 surfaces
• Projective models of Nikulin orbifolds
• On the motive of O'Grady's six dimensional hyper-Kähler varieties
• Derived-natural automorphisms on Hilbert schemes of points on generic K3 surfaces
• Some algebraic and geometric properties of hyper-Kähler fourfold symmetries