Higher direct images of dualizing sheaves of Lagrangian fibrations

By D. Matsushita. 2000

78 citations recorded by the source corpus.

We prove that the higher direct images of the dualizing sheaf of a Lagrangian fibration between smooth projective manifolds are isomorphic to the cotangent bundles of base space. As a corollary, we obtain that every Hodge number of the base space of a fibre space of an irreducible symplectic manifold is the same to that of a projective space if the base space is smooth.

Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/99094fe03c3e3ed2e8578941eebb84f7f821bffc

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Jun-Muk Hwang
2. E. Markman
3. Carolina Araujo

In Geometry and Topology

1. Jun-Muk Hwang
2. E. Markman
3. D. Huybrechts
4. Giovanni Mongardi
5. Misha Verbitsky
6. Nicolas Addington
7. D. Arapura
8. Ekaterina Amerik

In Statistical and Nonlinear Physics

1. Jun-Muk Hwang
2. E. Markman

Citations in the corpus

• Base manifolds for fibrations of projective irreducible symplectic manifolds (2007, result): “result of [ Ma3 ] verifies Theorem 1.1 (4), i.e., that the Betti numbers of X are indeed equal to those of Pn. Some special cases of this question were studied in [CMS, Section 7] and [Ng].”
• A survey of Torelli and monodromy results for holomorphic-symplectic varieties (2011, methodology): “We refer the reader also to the important work of Matsushita on Lagrangian fibrations [Mat1, Mat2 ] and to the survey ([Be2], section 1.6).”
• Abelian fibred holomorphic symplectic manifolds (2003, unknown): “It is now fairly easy to show that it is actually an elliptic bration overP1 (this fact has also been partially generalized in higher dimensions by Matsushita [32, 33 ]).”