nLab
symplectic singularity

Contents

Idea

A normal variety is called a symplectic variety? if its smooth part admits a holomorphic symplectic form, whose pull-back to any resolution extends to a holomorphic 2-form. If this 2-form is itself symplectic, the given resolution is called a symplectic resolution. More generally, an algebraic variety is said to have symplectic singularities if every point in the variety has a neighborhood which carries a symplectic structure.

Symplectic resolutions are analogous to hyper Kähler manifolds?.

References

The term was introduced in

Useful surveys include:

  • Dmitry Kaledin, Geometry and topology of symplectic resolutions, (arXiv/0608143)
  • Baohua Fu, A survey on symplectic singularities and symplectic resolution, Annales Mathématiques Blaise Pascal 13 (2006) (web)

from which some of the above text is taken.

Revised on February 22, 2012 20:49:29 by Ben Webster (129.10.73.95)