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

- Arnaud Beauville,
*Symplectic singularities*(1999) (arXiv:math/9903070)

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.