Base manifolds for fibrations of projective irreducible symplectic manifolds
By Jun-Muk Hwang. 2007
106 citations recorded by the source corpus.
Given a projective irreducible symplectic manifold M of dimension 2n, a projective manifold X and a surjective holomorphic map f:M→X with connected fibers of positive dimension, we prove that X is biholomorphic to the projective space of dimension n. The proof is obtained by exploiting two geometric structures at general points of X: the affine structure arising from the action variables of the Lagrangian fibration f and the structure defined by the variety of minimal rational tangents on the Fano manifold X.
Subfields: Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/e306ef9911ae055b4c7b92f7e5fd00259b1fb92a
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In Geometry and Topology
- Claire Voisin
- Valentino Tosatti
- Yuguang Zhang
- Mark Gross
- H. Hein
- M. Haskins
- Johannes Nordstrom
- A. Beauville
Citations in the corpus
- Gromov-Hausdorff collapsing of Calabi-Yau manifolds (2013, background): “Also, the base manifold N is always biholomorphic to CP [8, 16].”
- Asymptotically cylindrical Calabi-Yau manifolds (2012, background): “(In this situation, a much more difficult result due to Hwang [20] then asserts that B is projective space if both M and B are algebraic; these algebraicity hypotheses have very recently been removed by Greb and Lehn [15].”
- Remarks on degenerations of hyper-K\"ahler manifolds (2017, background): “For instance, if B is smooth, then B ∼= CPn by a theorem of Hwang [34].”
- Holomorphic symplectic geometry: a problem list (2010, background): “It is expected that 2) holds without the projectivity assumption on X (see the discussion in the introduction of [20]).”