A new six dimensional irreducible symplectic variety

2000/10/19 by Kieran G. O'Grady, Kieran G. O’Grady, O'Grady, Kieran G. · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Finite Group Theory Research #math.AG #math.DG #msc:14D20 #msc:53C55

paper · pdf · doi:10.48550/arxiv.math/0010187

68 pages

arxiv created 2000/10/19 · arxiv updated 2009/11/30

Abstract

By results of the author there exists a projective (holomorphic) symplectic desingularization of the moduli space of rank-two torsion-free sheaves on a genus-two Jacobian with c₁=0 and c₂=2. This desingularization has a natural map to the self-product of the Jacobian. We show that the fiber over (0,0) is a 6-dimensional projective irreducible symplectic variety (and hence a 12-dimensional compact Hyperkahler manifold) with second Betti number equal to 8. Thus it is not deformation equivalent to any of the (few) known examples of irreducible symplectic varieties, even up to birational equivalence.

Cited by

• From logarithmic Hilbert schemes to degenerations of hyperkähler varieties
• On anti-hyperbolicity for hyperkähler varieties
• Arithmetic monodromy of hyper-Kähler varieties over p-adic fields

Related

• Desingularized moduli spaces of sheaves on a K3, II
• Desingularized moduli spaces of sheaves on a K3, I
• Irreducible symplectic varieties with a large second Betti number
• Symplectic desingularization of moduli space of sheaves on a K3 surface
• Topological invariants of O'Grady's six dimensional irreducible symplectic variety