Results 31 to 40 of about 257,749 (139)
Teichmüller spaces and Torelli theorems for hyperkähler manifolds [PDF]
Kreck and Yang Su recently gave counterexamples to a version of the Torelli theorem for hyperkählerian manifolds as stated by Verbitsky. We extract the correct statement and give a short proof of it.
E. Looijenga
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
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
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
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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
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Limit Mixed Hodge Structures of Hyperkähler Manifolds [PDF]
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
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
Subquadratic harmonic functions on Calabi‐Yau manifolds with maximal volume growth
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
Corrigendum: Finiteness of polarized K3 surfaces and hyperkähler manifolds
In the proof of Proposition 2.8 in [Huy18] we consider isometric embeddings φ : T (S0) //T (S0)⊕ Z · e with φ(σ) ∈ C · σ⊕C · σ̄⊕C · e. At this point Lemma 2.5 is evoked, which, however, assumes the more restrictive and unrealistic condition (2.1) φC(σ)
D. Huybrechts
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