Automorphisms of O'Grady's Manifolds Acting Trivially on Cohomology

2014/11/04 by Giovanni Mongardi, Mongardi, Giovanni, Malte Wandel +1 · 1 citation
Mathematics · #14D06 #14F05 #14J50 #14K30 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14D06 #msc:14F05 #msc:14J50 #msc:14K30

paper · pdf · doi:10.48550/arxiv.1411.0759

16 pages. v2: study of the fixed loci added. section on the geometry of OG6 added (Section 3)

arxiv created 2015/04/03 · arxiv updated 2015/04/06

Abstract

We determine the subgroup of automorphisms acting trivially on the second integral cohomology for hyperkaehler manifolds which are deformation equivalent to O'Grady's sporadic examples. In particular, we prove that this subgroup is trivial in the ten dimensional case and isomorphic to (ℤ/2ℤ)^{× 8} in the six dimensional case. Furthermore we study the fixed loci of the automorphisms in the six dimensional case.

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