Degenerate twistor spaces for hyperkahler manifolds

作者：Verbitsky Misha^*

来源：Journal of Geometry and Physics, 2015, 91: 2-11.

DOI：10.1016/j.geomphys.2014.08.010

• Twistor space
• Hyperkahler manifold
• Lagrangian fibration
• Holomorphically symplectic manifold
• Special Lagrangian submanifold

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.

• 出版日期2015-5