Cotangent bundles of toric varieties and coverings of toric hyperkähler manifolds

Abstract

Toric hyperk{ä}hler manifolds are quaternion analog of toric varieties. Bielawski pointed out that they can be glued by cotangent bundles of toric varieties. Following his idea, viewing both toric varieties and toric hyperk{ä}her manifolds as GIT quotients, we first establish geometrical criteria for the semi-stable points. Then based on these criteria, we show that the cotangent bundles of compact toric varieties in the core of toric hyperk{ä}hler manifold are sufficient to glue the desired toric hyperk{ä}hler manifold.

16 pages, 4 figure

References in corpus (2)

• A survey of hypertoric geometry and topology
• Notes on GIT and symplectic reduction for bundles and varieties

Cited by in corpus (1)

• Fibred toric varieties in toric hyperkähler varieties