Results 1 to 10 of about 257,749 (139)
On Symplectic Birational Self-Maps of Projective Hyperkähler Manifolds of K3[n]-Type [PDF]
International mathematics research notices, 2022 We prove that projective hyperkähler manifolds of K3$^{[n]}$-type admitting a non-trivial symplectic birational self-map of finite order are isomorphic to moduli spaces of stable (twisted) coherent sheaves on K3 surfaces.
Yajnaseni Dutta +2 more
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Towards generic base-point-freeness for hyperkähler manifolds of generalized Kummer type
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg, 2022 We study base-point-freeness for big and nef line bundles on hyperkähler manifolds of generalized Kummer type: For $$n\in \{2,3,4\}$$ n ∈ { 2 , 3 , 4 } , we show that, generically in all but a finite number of irreducible components of the moduli space ...
Mauro Varesco
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A characterization of compact locally conformally hyperkähler manifolds [PDF]
Annali di Matematica Pura ed Applicata, 2019 We give an equivalent definition of compact locally conformally hyperkähler manifolds in terms of the existence of a non-degenerate complex two-form with natural properties.
Liviu Ornea, Alexandra Otiman
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Basic Remarks on Lagrangian Submanifolds of Hyperkähler Manifolds [PDF]
International mathematics research noticesThis note presents basic restrictions on the topology of Lagrangian surfaces of hyper-Kähler $4$-folds and a remark on the interaction of a Lagrangian subvariety of a hyper-Kähler variety with a Lagrangian fibration of the latter.
René Mboro
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On the Alesker-Verbitsky Conjecture on HyperKähler Manifolds [PDF]
Geometric and Functional Analysis, 2021 We solve the quaternionic Monge–Ampère equation on hyperKähler manifolds. In this way we prove the ansatz for the conjecture raised by Alesker and Verbitsky claiming that this equation should be solvable on any hyperKähler with torsion manifold, at least
S. Dinew, Marcin Sroka
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On the Image of the Period Map for Polarized Hyperkähler Manifolds [PDF]
International mathematics research notices, 2021 The moduli space for polarized hyperkähler manifolds of ${\textrm {K3}^{[m]}}$-type or ${\textrm {Kum}}_m$-type with a given polarization type is not necessarily connected, which is a phenomenon that only happens for $m$ large.
Jieao Song
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Einstein Metrics on Bundles over Hyperkähler Manifolds [PDF]
Communications in Mathematical Physics, 2021 We construct explicit examples of quaternion-Kähler and hypercomplex structures on bundles over hyperKähler manifolds. We study the infinitesimal symmetries of these examples and the associated Galicki–Lawson quaternion-Kähler moment map.
Udhav Fowdar
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Topological Bounds on Hyperkähler Manifolds [PDF]
Experimental Mathematics, 2021 We conjecture that certain curvature invariants of compact hyperkähler manifolds are positive/negative. We prove the conjecture in complex dimension four, give an “experimental proof” in higher dimensions, and verify it for all known hyperkähler ...
Justin Sawon
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Calibrated geometry in hyperkähler cones, 3-Sasakian manifolds, and twistor spaces [PDF]
Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2023 We systematically study calibrated geometry in hyperkähler cones $C^{4n+4}$ , their 3-Sasakian links $M^{4n+3}$ , and the corresponding twistor spaces $Z^{4n+2}$ , emphasizing the relationships between submanifold geometries in various spaces.
Benjamin Aslan +2 more
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Stratification of singular hyperkähler quotients
Complex Manifolds, 2022 Hyperkähler quotients by non-free actions are typically singular, but are nevertheless partitioned into smooth hyperkähler manifolds. We show that these partitions are topological stratifications, in a strong sense.
Mayrand Maxence
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