Degenerate twistor spaces for hyperkahler manifolds

JOURNAL OF GEOMETRY AND PHYSICS

卷:91

Article

Verbitsky, Misha^1,2 

[1] NRU HSE, Fac Math, Lab Algebra Geometry, Moscow, Russia

[2] Univ Tokyo, Kavli IPMU WPI, Tokyo 1138654, Japan

关键词: Twistor space;    Hyperkahler manifold;    Lagrangian fibration;    Holomorphically symplectic manifold;    Special Lagrangian submanifold;   

DOI  :  10.1016/j.geomphys.2014.08.010

来源: Elsevier

【 摘 要 】

Let M be a hyperkahler manifold, and eta a closed, positive (1, 1)-form with rk eta < dim M. We associate to eta a family of complex structures on M, called a degenerate twistor family, and parametrized by a complex line. When eta is a pullback of a Kahler form under a Lagrangian fibration L, all the fibers of degenerate twistor family also admit a Lagrangian fibration, with the fibers isomorphic to that of L. Degenerate twistor families can be obtained by taking limits of twistor families, as one of the Kahler forms in the hyperkahler triple goes to eta. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

Free