nLab symplectic singularity




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?.


The term was introduced in

Useful surveys include:

  • Dmitry Kaledin, Geometry and topology of symplectic resolutions, Algebraic Geometry: 2005 Summer Research Institute, edited by Dan Abramovich (arXiv:math.AG/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.

Last revised on October 23, 2023 at 23:15:16. See the history of this page for a list of all contributions to it.