On isotropic divisors on irreducible symplectic manifolds. (English) Zbl 1392.32009

Matsushita, Daisuke

Oguiso, Keiji (ed.) et al., Higher dimensional algebraic geometry. In honour of Professor Yujiro Kawamata’s sixtieth birthday. Proceedings of the conference, Tokyo, Japan, January 7–11, 2013. Tokyo: Mathematical Society of Japan (MSJ) (ISBN 978-4-86497-046-4/hbk). Advanced Studies in Pure Mathematics 74, 291-312 (2017).

Summary: Let \(X\) be an irreducible symplectic manifold and \(L\) a divisor on \(X\). Assume that \(L\) is isotropic with respect to the Beauville-Bogomolov quadratic form. We define the rational Lagrangian locus and the movable locus on the universal deformation space of the pair \((X, L)\). We prove that the rational Lagrangian locus is empty or coincides with the movable locus of the universal deformation space.
For the entire collection see [Zbl 1388.14012].

MSC:

32Q15	Kähler manifolds
53D12	Lagrangian submanifolds; Maslov index

Keywords:

Kähler manifold; symplectic manifold; Lagrangian fibration