A global Torelli theorem for hyperkaehler manifolds (after Verbitsky)
By D. Huybrechts. 2011
59 citations recorded by the source corpus.
Compact hyperkaehler manifolds are higher-dimensional generalizations of K3 surfaces. The classical Global Torelli theorem for K3 surfaces, however, does not hold in higher dimensions. More precisely, a compact hyperkaehler manifold is in general not determined by its natural weight-two Hodge structure. The text gives an account of a recent theorem of M. Verbitsky, which can be regarded as a weaker version of the Global Torelli theorem phrased in terms of the injectivity of the period map on the connected components of the moduli space of marked manifolds.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ea4ddf10134e3612ab3204cf41f3223832548eb6
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In Geometry and Topology
- E. Markman
- Keiji Oguiso
- D. Huybrechts
- Giovanni Mongardi
- Misha Verbitsky
- A. Sarti
- Nicolas Addington
- Samuel Boissière
In Mathematical Physics
- Keiji Oguiso
- E. Markman
- D. Huybrechts
- Misha Verbitsky
- Nicolas Addington
- Giovanni Mongardi
- D. Arapura
- Samuel Boissière
Citations in the corpus
- Lagrangian Fibrations of Holomorphic-Symplectic Varieties of K3[n]-Type (2013, methodology): “(The Global Torelli Theorem [Ver1, Hu3] ) The period map P 0 ∶ M 0Λ → Ω Λ is surjective.”
- Automorphism groups of Calabi-Yau manifolds of Picard number two (2012, methodology): “ by using Markman’s solution ([Ma11]) of weak version of the movable cone conjecture, after the global Torelli type results for hyperk¨ahler manifolds due to Huybrechts and Verbitsky ([Hu99], [Ve09], [Hu11]). Theorem (1.3) (3) is proved in Section 5 by using the surjectivity of the period map for hy”