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PARABOLIC AUTOMORPHISMS OF HYPERKÄHLER MANIFOLDS: ORBITS AND BETTI MAPS

Ekaterina Amerik, Serge Cantat
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Examples of Non-Rigid, Modular Vector Bundles on Hyperkähler Manifolds

International mathematics research notices, 2023
We exhibit examples of slope-stable and modular vector bundles on a hyperkähler manifold of K3$^{[2]}$-type, which move in a 20-dimensional family and study their algebraic properties.
Enrico Fatighenti
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On numerically trivial automorphisms of compact hyperkähler manifolds of dimension 4

Mathematical Research Letters, 2023
We prove that the automorphism group of a compact hyperk\"ahler manifold of dimension 4 acts faithfully on the cohomology ring.
Chen Jiang, Wenfei Liu
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Rational Curves and MBM Classes on Hyperkähler Manifolds: A Survey

Rationality of Varieties, 2020
This paper deals with rational curves and birational contractions on irreducible holomorphically symplectic manifold. We survey some recent results about minimal rational curves, their deformations, extremal rays associated with these curves, and the ...
E. Amerik, M. Verbitsky
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A compactness theorem for hyperkähler 4-manifolds with boundary

Duke mathematical journal, 2022
In this paper, we study the compactness of a boundary value problem for hyperkaehler 4-manifolds. We show that under certain topological conditions and the positive mean curvature condition on the boundary, a sequence of hyperkaehler triples converges ...
Hongying Liu
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Finiteness of Klein actions and real structures on compact hyperkähler manifolds

Mathematische Annalen, 2018
One central problem in real algebraic geometry is to classify the real structures of a given complex manifold. We address this problem for compact hyperkähler manifolds by showing that any such manifold admits only finitely many real structures up to ...
A. Cattaneo, L. Fu
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Contraction centers in families of hyperkähler manifolds

Selecta Mathematica, 2019
We study the exceptional loci of birational (bimeromorphic) contractions of a hyperkähler manifold M. Such a contraction locus is the union of all minimal rational curves in a collection of cohomology classes which are orthogonal to a wall of the Kähler ...
E. Amerik, M. Verbitsky
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Errata for “Mapping class group and a global Torelli theorem for hyperkähler manifolds” by Misha Verbitsky

Duke mathematical journal, 2020

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K-Theory of Toric HyperKähler Manifolds

Indian journal of pure and applied mathematics, 2020
V. Uma
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The parabolic quaternionic Calabi–Yau equation on hyperkähler manifolds

Revista matemática iberoamericana
Lucio Bedulli, Giovanni Gentili, Luigi Vezzoni   +2 more
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