scholarly journals Contraction centers in families of hyperkähler manifolds

2021 ◽  
Vol 27 (4) ◽  
Author(s):  
Ekaterina Amerik ◽  
Misha Verbitsky
Keyword(s):  
Hyperkähler Manifolds

A FAMILY OF HYPERKÄHLER MANIFOLDS

1994 ◽  
Vol 45 (4) ◽  
pp. 463-478 ◽  
Author(s):  
ANDREW S. DANCER
Keyword(s):  
Hyperkähler Manifolds

scholarly journals Isometries of Ideal Lattices and Hyperkähler Manifolds

2015 ◽  
Vol 2016 (4) ◽  
pp. 963-977 ◽  
Author(s):  
Samuel Boissière ◽  
Chiara Camere ◽  
Giovanni Mongardi ◽  
Alessandra Sarti
Keyword(s):  
Ideal Lattices ◽  
Hyperkähler Manifolds

Compact Tori Associated to Hyperkähler Manifolds of Kummer Type

2019 ◽  
Author(s):  
Kieran G O’Grady
Keyword(s):  
Open Subset ◽  
Parallel Transport ◽  
Linear Section ◽  
Linear Subspaces ◽  
Hyperkähler Manifolds ◽  
Hyperkähler Manifold ◽  
Weil Type ◽  
Compact Tori ◽  
Intermediate Jacobian

Abstract Dedicato alla piccola Mia. For $X$ a hyperkähler manifold of Kummer type, let $J^3(X)$ be the intermediate Jacobian associated to $H^3(X)$. We prove that $H^2(X)$ can be embedded into $H^2(J^3(X))$. We show that there exists a natural smooth quadric $Q(X)$ in the projectivization of $H^3(X)$, such that Gauss–Manin parallel transport identifies the set of projectivizations of $H^{2,1}(Y)$, for $Y$ a deformation of $X$, with an open subset of a linear section of $Q^{+}(X)$, one component of the variety of maximal linear subspaces of $Q(X)$. We give a new proof of a result of Mongardi restricting the action of monodromy on $H^2(X)$. Lastly, we show that if $X$ is projective, then $J^3(X)$ is an abelian fourfold of Weil type.

scholarly journals QUATERNIONIC KAHLER MANIFOLDS OF COHOMOGENEITY ONE

1999 ◽  
Vol 10 (05) ◽  
pp. 541-570 ◽  
Author(s):  
ANDREW DANCER ◽  
ANDREW SWANN
Keyword(s):  
Simple Group ◽  
Lie Algebras ◽  
Complex Structure ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Cohomogeneity One ◽  
Cohomogeneity One Action ◽  
Hyperkähler Manifolds ◽  
Adjoint Orbits ◽  
Quaternionic Kähler

Classification results are given for (i) compact quaternionic Kähler manifolds with a cohomogeneity-one action of a semi-simple group, (ii) certain complete hyperKähler manifolds with a cohomogeneity-two action of a semi-simple group preserving each complex structure, (iii) compact 3-Sasakian manifolds which are cohomogeneity one with respect to a group of 3-Sasakian symmetries. Information is also obtained about non-compact quaternionic Kähler manifolds of cohomogeneity one and the cohomogeneity of adjoint orbits in complex semi-simple Lie algebras.

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