Results 51 to 60 of about 257,471 (64)

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
semanticscholar   +1 more source

Hyperkähler Metrics on Cotangent Bundles of Hermitian Symmetric Spaces

, 2021
The cotangent bundle M = T ∗Σ of a complex manifold Σ is a holomorphicsymplectic manifold. If Σ is a generalized flag manifold, then this holomorphicsymplectic structure underlies a hyperkähler metric, whose restriction to Σ is the given homogeneous ...
O. Biquard, P. Gauduchon
semanticscholar   +1 more source

Picard number of the generic fiber of an abelian fibered hyperkähler manifold

, 2008
We shall show that the Picard number of the generic fiber of an abelian fibered hyperkähler manifold over the projective space is always one. We then give a few applications for the Mordell-Weil group. In particular, by deforming O’Grady’s 10-dimensional
K. Oguiso
semanticscholar   +1 more source

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
semanticscholar   +1 more source

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
semanticscholar   +1 more source

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
semanticscholar   +1 more source

On Donaldson’s flow of surfaces in a hyperkähler four-manifold

, 2006
We prove some basic properties of Donaldson’s flow of surfaces in a hyperkähler 4-manifold. When the initial submanifold is symplectic with respect to one Kähler form and Lagrangian with respect to another, we show that certain kinds of singularities ...
Jian Song, B. Weinkove
semanticscholar   +1 more source

On vector bundles over hyperkähler twistor spaces

Mathematische Zeitschrift, 2021
I. Biswas, A. Tomberg
semanticscholar   +1 more source

Twistor space of a generalized quaternionic manifold

Proceedings - Mathematical Sciences, 2021
G. Deschamps
semanticscholar   +1 more source

INDEFINITE HYPERKÄHLER METRICS ON LIE GROUPS WITH ABELIAN COMPLEX STRUCTURES

Transformation groups, 2020
I. Bajo, E. Sanmartín
semanticscholar   +2 more sources