On families of lagrangian tori on hyperkahler manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:71

Article

Amerik, Ekaterina^1,2  Campana, Frederic^3,4 

[1] Univ Paris 11, F-91405 Orsay, France

[2] Natl Res Univ, Higher Sch Econ, Dept Math, Lab Algebra Geometry, Moscow 117332, Russia

[3] Univ Henri Poincare, Inst Elie Cartan, F-54506 Vandoeuvre Les Nancy, France

[4] Inst Univ France, Paris, France

关键词: Holomorphic symplectic variety;    Lagrangian torus;    Fibration;   

DOI  :  10.1016/j.geomphys.2013.04.004

来源: Elsevier

【 摘 要 】

This is a note on Beauville's problem (solved by Greb, Lehn, and Rollenske in the non-algebraic case, and by Hwang and Weiss in general) whether a lagrangian torus on an irreducible holomorphic symplectic manifold is a fiber of a lagrangian fibration. We provide a different Very short solution in the non-algebraic case, and make some observations suggesting a different approach in the algebraic case. (C) 2013 Elsevier B.V. All rights reserved.

【 授权许可】

Free