Toric Hyperkahler Varieties
| dc.creator | Hausel, Tamas | |
| dc.creator | Sturmfels, Bernd | |
| dc.date | 2002-03-11 | |
| dc.date | 2002-04-30 | |
| dc.date.accessioned | 2026-07-07T04:46:57Z | |
| dc.date.available | 2026-07-07T04:46:57Z | |
| dc.description | Extending work of Bielawski-Dancer and Konno, we develop a theory of toric hyperkahler varieties, which involves toric geometry, matroid theory and convex polyhedra. The framework is a detailed study of semi-projective toric varieties, meaning GIT quotients of affine spaces by torus actions, and specifically, of Lawrence toric varieties, meaning GIT quotients of even-dimensional affine spaces by symplectic torus actions. A toric hyperkahler variety is a complete intersection in a Lawrence toric variety. Both varieties are non-compact, and they share the same cohomology ring, namely, the Stanley-Reisner ring of a matroid modulo a linear system of parameters. Familiar applications of toric geometry to combinatorics, including the Hard Lefschetz Theorem and the volume polynomials of Khovanskii-Pukhlikov, are extended to the hyperkahler setting. When the matroid is graphic, our construction gives the toric quiver varieties, in the sense of Nakajima. | |
| dc.description | 32 pages, Latex; minor corrections and a reference added | |
| dc.identifier | https://arxiv.org/abs/math/0203096 | |
| dc.identifier | http://arxiv.org/abs/math/0203096 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63535 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | Differential Geometry | |
| dc.title | Toric Hyperkahler Varieties | |
| dc.type | text |