The Geometry of Toric Hyperk\"ahler Varieties
Hiroshi Konno
TL;DR
This survey explores the geometric properties of toric hyperk"ahler varieties, focusing on their Betti numbers, cohomology rings, and structural variations, providing improved results and proofs.
Contribution
It offers a comprehensive overview of the geometry of toric hyperk"ahler varieties with new insights and refined proofs of key properties.
Findings
Detailed descriptions of Betti numbers and cohomology rings.
Analysis of variation of hyperk"ahler structures.
Improved proofs of geometric properties.
Abstract
In this survey article we describe the geometry of toric hyperk\"ahler varieties, which are hyperk\"ahler quotients of the quaternionic vector spaces by tori. In particular, we discuss the Betti numbers, the cohomology ring, and variation of hyperk\"ahler structures of these spaces with many improved results and proofs.
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Taxonomy
TopicsGeometry and complex manifolds · Natural Compound Pharmacology Studies · Algebraic Geometry and Number Theory