Hyper-Kähler Manifolds

Debarre, Olivier

doi:10.1007/s00032-022-00366-x

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2022

2024

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Cited by 8 publications

(1 citation statement)

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“…In particular for n " 2 (and g " l " 1) Theorem 1.1 reduces to the main result in [O'G22]. Note also that in this case K il e p2nq is irreducible by [Deb22, Theorem 3.5], and hence K il e p2nq good " K il e p2nq.…”

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confidence: 77%

Rigid stable vector bundles on hyperkähler varieties of type $K3^{[n]}$

O’Grady¹

2022

Preprint

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We prove existence and unicity results for slope stable vector bundles on a general polarized hyperkähler (HK) variety of type K3 rns with certain discrete invariants, provided the rank and the first two Chern classes of the vector bundle satisfy certain equalities. The latter hypotheses at first glance appear to be quite restrictive, but we suspect that we have listed almost all slope stable rigid projectively hyperholomorphic vector bundles on polarized HK varieties of type K3 rns with 20 moduli.

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confidence: 77%

Rigid stable vector bundles on hyperkähler varieties of type $K3^{[n]}$

O’Grady¹

2022

Preprint

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Some motivic properties of Gushel–Mukai sixfolds

Bolognesi,

Laterveer

2023

Mathematische Nachrichten

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Gushel–Mukai (GM) sixfolds are an important class of so‐called Fano‐K3 varieties. In this paper, we show that they admit a multiplicative Chow–Künneth decomposition modulo algebraic equivalence and that they have the Franchetta property. As side results, we show that double Eisenbud‐Popescu‐Walter (EPW) sextics and cubes have the Franchetta property, modulo algebraic equivalence, and some vanishing results for the Chow ring of GM sixfolds.

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Groups Acting on Moduli Spaces of Hyper-Kähler Manifolds

Rizzo

2024

Milan J. Math.

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Hyper-Kähler Manifolds

Cited by 8 publications

References 89 publications

Rigid stable vector bundles on hyperkähler varieties of type $K3^{[n]}$

Rigid stable vector bundles on hyperkähler varieties of type $K3^{[n]}$

Some motivic properties of Gushel–Mukai sixfolds

Groups Acting on Moduli Spaces of Hyper-Kähler Manifolds

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