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O'Grady's tenfolds from stable bundles on hyper-K\"ahler fourfolds
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abstract
We provide a modular construction of the Laza--Sacc\`a--Voisin compactification of the intermediate Jacobian fibration of a cubic fourfold. Additionally, we construct infinitely many $20$-dimensional families of polarized hyper-K\"ahler manifolds of type OG10, realized as moduli spaces of stable bundles on hyper-K\"ahler manifolds of type $\mathrm{K3}^{[2]}$.
Forward citations
Cited by 2 Pith papers
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Hodge numbers of a Fano eightfold of K3 type
The Hodge numbers of a Fano eightfold of index three of K3 type are computed via a semistable degeneration, yielding Picard rank one; a secant-line model of the Hilbert square of a genus-eight K3 is also derived.
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Deformations of twisted sheaves and formality results
Twisted sheaf deformations are controlled by RHom with formality for polystable twisted sheaves on Kodaira-dimension-0 minimal surfaces and projectively hyper-holomorphic twisted bundles on hyper-Kähler manifolds.
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