Results 21 to 30 of about 257,471 (64)
Hyperkähler metrics near Lagrangian submanifolds and symplectic groupoids [PDF]
The first part of this paper is a generalization of the Feix–Kaledin theorem on the existence of a hyperkähler metric on a neighborhood of the zero section of the cotangent bundle of a Kähler manifold.
Maxence Mayrand
semanticscholar +1 more source
Special Joyce structures and hyperkähler metrics [PDF]
Joyce structures were introduced by T. Bridgeland in the context of the space of stability conditions of a three-dimensional Calabi–Yau category and its associated Donaldson–Thomas invariants. In subsequent work, T. Bridgeland and I. Strachan showed that
Iván Tulli
semanticscholar +1 more source
Compact Tori Associated to Hyperkähler Manifolds of Kummer Type [PDF]
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 $H^2(J^3(X))$.
K. O’Grady
semanticscholar +1 more source
Canonical complex extensions of Kähler manifolds
Abstract Given a complex manifold X, any Kähler class defines an affine bundle over X, and any Kähler form in the given class defines a totally real embedding of X into this affine bundle. We formulate conditions under which the affine bundles arising this way are Stein and relate this question to other natural positivity conditions on the tangent ...
Daniel Greb, Michael Lennox Wong
wiley +1 more source
On the Hodge structures of compact hyperkähler manifolds [PDF]
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
MBM classes and contraction loci on low-dimensional hyperkähler manifolds of K3${}^{[n]}$ type [PDF]
An MBM locus on a hyperkahler manifold is the union of all deformations of a minimal rational curve with negative self-intersection. MBM loci can be equivalently defined as centers of bimeromorphic contractions.
E. Amerik, M. Verbitsky
semanticscholar +1 more source
Among other things, we show that Mordell-Weil groups of finitely many different abelian fibrations of a hyperkahler manifold have essentially no relation, as its bira- tional transformation.
K. Oguiso
semanticscholar +1 more source
Collapsing hyperkähler manifolds [PDF]
Given a projective hyperkahler manifold with a holomorphic Lagrangian fibration, we prove that hyperkahler metrics with volume of the torus fibers shrinking to zero collapse in the Gromov-Hausdorff sense (and smoothly away from the singular fibers) to a ...
Valentino Tosatti, Yuguang Zhang
semanticscholar +1 more source
Curvature of quaternionic skew‐Hermitian manifolds and bundle constructions
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
Characteristic foliations — A survey
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