scholarly journals L 2 -Cohomology of Hyperkähler Quotients

2000 ◽  
Vol 211 (1) ◽  
pp. 153-165 ◽  
Author(s):  
Nigel Hitchin
Keyword(s):  
Hyperkahler Quotients

scholarly journals Hyperkähler quotients and algebraic curves

2000 ◽  
Vol 2000 (01) ◽  
pp. 022-022 ◽  
Author(s):  
Ulf Lindström ◽  
Martin Rocek ◽  
Rikard von Unge
Keyword(s):  
Algebraic Curves ◽  
Hyperkahler Quotients

Curvature of hyperkähler quotients

2008 ◽  
Vol 6 (2) ◽  
pp. 191-203
Author(s):  
Roger Bielawski
Keyword(s):  
Hyperkahler Quotients

CLASSICAL NILPOTENT ORBITS AS HYPERKÄHLER QUOTIENTS

1996 ◽  
Vol 07 (02) ◽  
pp. 193-210 ◽  
Author(s):  
PIOTR Z. KOBAK ◽  
ANDREW SWANN
Keyword(s):  
Lie Algebras ◽  
Direct Proof ◽  
Classical Case ◽  
Nilpotent Orbits ◽  
Kahler Geometry ◽  
Complex Semisimple ◽  
Low Dimensional ◽  
Hyperkahler Quotients ◽  
Kahler Quotients ◽  
Quaternionic Kähler

We show that on an arbitrary nilpotent orbit [Formula: see text] in [Formula: see text] where [Formula: see text] is a direct sum of classical simple Lie algebras, there is a G-invariant hyperKähler structure obtainable as a hyperKäher quotient of the flat hyperKähler manifold ℝ4N≅ℍN. Coïncidences between various low-dimensional simple Lie groups lead to some nilpotent orbits being described as hyperKähler quotients (in some cases in fact finite quotients) of other nilpotent orbits. For example, from the construction we are able to read off pairs of orbits [Formula: see text] in different classical Lie algebras [Formula: see text] such that there is a finite [Formula: see text]-equivariant surjection [Formula: see text] between the orbit closures. We include a table listing examples of hyperKähler quotients between small nilpotent orbits. The above-mentioned results have consequences in quaternionic Kähler geometry: it is known that nilpotent orbits in complex semisimple Lie algebras give rise to quaternionic Kähler manifolds. Our approach gives a more direct proof of this in the classical case as these manifolds turn out to be quaternionic Kähler quotients of quaternionic projective spaces. We find that many of these manifolds can also be constructed as quaternionic Kähler quotients of complex Grassmannians [Formula: see text].

scholarly journals On the cohomology of hyperkähler quotients

2009 ◽  
Vol 14 (4) ◽  
pp. 801-823 ◽  
Author(s):  
Lisa Jeffrey ◽  
Young-Hoon Kiem ◽  
Frances Kirwan
Keyword(s):  
Hyperkahler Quotients

scholarly journals ORBIFOLD COHOMOLOGY OF HYPERTORIC VARIETIES

2008 ◽  
Vol 19 (08) ◽  
pp. 927-956 ◽  
Author(s):  
REBECCA F. GOLDIN ◽  
MEGUMI HARADA
Keyword(s):  
Affine Space ◽  
Hyperplane Arrangement ◽  
Betti Numbers ◽  
Hyperplane Arrangements ◽  
Euler Characteristics ◽  
Combinatorial Description ◽  
Orbifold Cohomology ◽  
Hypertoric Varieties ◽  
Hyperkahler Quotients ◽  
Combinatorial Data

Hypertoric varieties are hyperkähler analogues of toric varieties, and are constructed as abelian hyperkähler quotients T*ℂn//// T of a quaternionic affine space. Just as symplectic toric orbifolds are determined by labelled polytopes, orbifold hypertoric varieties are intimately related to the combinatorics of hyperplane arrangements. By developing hyperkähler analogues of symplectic techniques developed by Goldin, Holm, and Knutson, we give an explicit combinatorial description of the Chen–Ruan orbifold cohomology of an orbifold hypertoric variety in terms of the combinatorial data of a rational cooriented weighted hyperplane arrangement [Formula: see text]. We detail several explicit examples, including some computations of orbifold Betti numbers (and Euler characteristics).

scholarly journals Hyperkahler quotients, mirror symmetry, and F-theory

2000 ◽  
Vol 2000 (03) ◽  
pp. 037-037 ◽  
Author(s):  
Inyong Y Park ◽  
Rikard von Unge
Keyword(s):  
Mirror Symmetry ◽  
Hyperkahler Quotients

scholarly journals Abelianization for hyperkähler quotients

Topology ◽  
2005 ◽  
Vol 44 (1) ◽  
pp. 231-248 ◽  
Author(s):  
Tamás Hausel ◽  
Nicholas Proudfoot
Keyword(s):  
Hyperkahler Quotients

Erratum to “Curvature of hyperkähler quotients”

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Roger Bielawski
Keyword(s):  
Original Version ◽  
Central European Journal ◽  
Central European ◽  
Hyperkahler Quotients

AbstractThe original version of the article was published in Central European Journal of Mathematics, 2008, 6(2), 191–203, DOI: 10.2478/s11533-008-0026-8. Unfortunately, the original version of this article contains a mistake, which we correct here.

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