On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties

Felisetti, Camilla; Shen, Junliang; Yin, Qizheng

doi:10.1090/tran/8592

Cited by 5 publications

(3 citation statements)

References 30 publications

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“…Knowing birational models of irreducible holomorphic symplectic (ihs) manifolds is a significant step toward the full comprehension of their geometry. In recent years, the birational geometry of ihs manifolds and their deformation theory have had extensive applications in many fields of algebraic geometry: not only they are a fundamental tool for hunting new examples of ihs varieties in both the smooth and singular case (see, for example, [5,35]), but also they turned out to be one of the key ingredients in the investigation of P=W phenomena arising from non-abelian Hodge theory; see, for example, [10,11,12,48]. Many examples of ihs manifolds are realized from moduli spaces of sheaves on abelian or K3 surfaces.…”

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confidence: 99%

O’Grady tenfolds as moduli spaces of sheaves

Felisetti,

Giovenzana,

Grossi

2024

Forum of Mathematics, Sigma

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We give a lattice-theoretic characterization for a manifold of $\operatorname {\mathrm {OG10}}$ type to be birational to some moduli space of (twisted) sheaves on a K3 surface. We apply it to the Li–Pertusi–Zhao variety of $\operatorname {\mathrm {OG10}}$ type associated to any smooth cubic fourfold. Moreover, we determine when a birational transformation is induced by an automorphism of the K3 surface, and we use this to classify all induced birational symplectic involutions.

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confidence: 99%

O’Grady tenfolds as moduli spaces of sheaves

Felisetti,

Giovenzana,

Grossi

2024

Forum of Mathematics, Sigma

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“…The perverse-Hodge symmetry. The motivation for Conjecture 0.1 is an effort to understand and categorify the perverse-Hodge symmetry for Lagrangian fibrations [31]; see also [11,10,16,32].…”

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confidence: 99%

Fourier-Mukai transforms and the decomposition theorem for integrable systems

Maulik¹,

Shen²,

Yin³

2023

Preprint

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We study the interplay between the Fourier-Mukai transform and the decomposition theorem for an integrable system π : M → B. Our main conjecture is that the Fourier-Mukai transform of sheaves of Kähler differentials, after restriction to the formal neighborhood of the zero section, are quantized by the Hodge modules arising in the decomposition theorem for π. For an integrable system, our formulation unifies the Fourier-Mukai calculation of the structure sheaf by Arinkin-Fedorov, the theorem of the higher direct images by Matsushita, and the "perverse = Hodge" identity by the second and the third authors.As evidence, we show that these Fourier-Mukai images are Cohen-Macaulay sheaves with middle-dimensional support on the relative Picard space, with support governed by the higher discriminants of the integrable system. We also prove the conjecture for smooth integrable systems and certain 2-dimensional families with nodal singular fibers. Finally, we sketch the proof when cuspidal fibers appear.

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“…Restriction to smooth fibres. Let M be a projective irreducible holomorphic symplectic variety of dimension 2r equipped with a Lagrangian fibration f : M → B. In[28] Felisetti, Shen and Yin have proved that the restriction of H * (M, Q) to a smooth fiber of f is isomorphic to H * (P r , Q). In general, this is false for non-compact hyperkähler varieties, but it holds true for the Hitchin fibration for n > 1 by [1, Thm 5], up to a copy of H • (C, Q).…”

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confidence: 99%

Hodge-to-singular correspondence for reduced curves

Mauri¹,

Migliorini²

2022

Preprint

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We study the summands of the decomposition theorem for the Hitchin system for GLn, in arbitrary degree, over the locus of reduced spectral curves. A key ingredient is a new correspondence between these summands and the topology of hypertoric quiver varieties. In contrast to the case of meromorphic Higgs fields, the intersection cohomology groups of moduli spaces of regular Higgs bundles depend on the degree. We describe this dependence.

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On intersection cohomology and Lagrangian fibrations of irreducible symplectic varieties

Cited by 5 publications

References 30 publications

O’Grady tenfolds as moduli spaces of sheaves

O’Grady tenfolds as moduli spaces of sheaves

Fourier-Mukai transforms and the decomposition theorem for integrable systems

Hodge-to-singular correspondence for reduced curves

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