Results 41 to 50 of about 261,915 (134)
The intrinsic torsion of almost quaternion-Hermitian manifolds [PDF]
, 2007 We study the intrinsic torsion of almost quaternion-Hermitian manifolds via the exterior algebra. In particular, we show how it is determined by particular three-forms formed from simple combinations of the exterior derivatives of the local Kaehler forms.
Cabrera, Francisco Martin, Swann, Andrew
core +1 more source
The indeterminacy locus of the Voisin map
, 2019 Beauville and Donagi proved that the variety of lines $F(Y)$ of a smooth cubic fourfold $Y$ is a hyperk\"ahler variety. Recently, C. Lehn, M.Lehn, Sorger and van Straten proved that one can naturally associate a hyperK\"ahler variety $Z(Y)$ to the ...
Muratore, Giosuè Emanuele
core +1 more source
Limit Mixed Hodge Structures of Hyperkähler Manifolds [PDF]
Moscow Mathematical Journal, 2018 This note is inspired by the work of Deligne on the local behavior of Hodge structures at infinity. We study limit mixed Hodge structures of degenerating families of compact hyperk\"ahler manifolds.
A. Soldatenkov
semanticscholar +1 more source
On the Hodge structures of compact hyperkähler manifolds [PDF]
, 2019 The purpose of this note is to give an account of a well-known folklore result: the Hodge structure on the second cohomology of a compact hyperk\"ahler manifold uniquely determines Hodge structures on all higher cohomology groups.
A. Soldatenkov
semanticscholar +1 more source
The symplectic density property for Calogero–Moser spaces
Journal of the London Mathematical Society, Volume 111, Issue 2, February 2025.Abstract We introduce the symplectic density property and the Hamiltonian density property together with the corresponding versions of Andersén–Lempert theory. We establish these properties for the Calogero–Moser space Cn$\mathcal {C}_n$ of n$n$ particles and describe its group of holomorphic symplectic automorphisms.
Rafael B. Andrist, Gaofeng Huang
wiley +1 more source
Limits of Riemannian 4-manifolds and the symplectic geometry of their twistor spaces
, 2016 The twistor space of a Riemannian 4-manifold carries two almost complex structures, $J_+$ and $J_-$, and a natural closed 2-form $\omega$. This article studies limits of manifolds for which $\omega$ tames either $J_+$ or $J_-$.
Fine, Joel
core +1 more source
Curvature of quaternionic skew‐Hermitian manifolds and bundle constructions
Mathematische Nachrichten, Volume 298, Issue 1, Page 87-112, January 2025.Abstract This paper is devoted to a description of the second‐order differential geometry of torsion‐free almost quaternionic skew‐Hermitian manifolds, that is, of quaternionic skew‐Hermitian manifolds (M,Q,ω)$(M, Q, \omega)$. We provide a curvature characterization of such integrable geometric structures, based on the holonomy theory of symplectic ...
Ioannis Chrysikos +2 more
wiley +1 more source
HyperK\"ahler Potentials via Finite-Dimensional Quotients
, 2000 It is known that nilpotent orbits in a complex simple Lie algebra admit hyperK\"ahler metrics with a single function that is a global potential for each of the K\"ahler structures (a hyperK\"ahler potential).
Kobak, Piotr, Swann, Andrew
core +2 more sources
Characteristic foliations — A survey
Bulletin of the London Mathematical Society, Volume 56, Issue 7, Page 2231-2249, July 2024.Abstract This is a survey article, with essentially complete proofs, of a series of recent results concerning the geometry of the characteristic foliation on smooth divisors in compact hyperkähler manifolds, starting with work by Hwang–Viehweg, but also covering articles by Amerik–Campana and Abugaliev.
Fabrizio Anella, Daniel Huybrechts
wiley +1 more source
Subquadratic harmonic functions on Calabi‐Yau manifolds with maximal volume growth
Communications on Pure and Applied Mathematics, Volume 77, Issue 6, Page 3080-3106, June 2024.Abstract On a complete Calabi‐Yau manifold M$M$ with maximal volume growth, a harmonic function with subquadratic polynomial growth is the real part of a holomorphic function. This generalizes a result of Conlon‐Hein. We prove this result by proving a Liouville‐type theorem for harmonic 1‐forms, which follows from a new local L2$L^2$ estimate of the ...
Shih‐Kai Chiu
wiley +1 more source