Abstract
We study the hypersymplectic spaces obtained as quotients of flat hypersymplectic space ℝ4d by the action of a compact Abelian group. These 4n-dimensional quotients carry a multi-Hamilitonian action of an ntorus. The image of the hypersymplectic moment map for this torus action may be described by a configuration of solid cones in ℝ3n. We give precise conditions for smoothness and non-degeneracy of such quotients and show how some properties of the quotient geometry and topology are constrained by the combinatorics of the cone configurations. Examples are studied, including non-trivial structures on ℝ4n and metrics on complements of hypersurfaces in compact manifolds.
| Original language | English |
|---|---|
| Journal | Transactions of the American Mathematical Society |
| Volume | 359 |
| Issue | 3 |
| Pages (from-to) | 1265-1284 |
| Number of pages | 20 |
| ISSN | 0002-9947 |
| DOIs | |
| Publication status | Published - 1 Mar 2007 |
| Externally published | Yes |
Keywords
- Hypersymplectic structure
- Moment map
- Neutral hyperkähler manifold
- Toric variety