Hyperpolygon spaces and their cores
Authors:
Megumi Harada and Nicholas Proudfoot
Journal:
Trans. Amer. Math. Soc. 357 (2005), 14451467
MSC (2000):
Primary 53C26; Secondary 16G20, 14D20
Published electronically:
September 23, 2004
MathSciNet review:
2115372
Fulltext PDF Free Access
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Abstract: Given an tuple of positive real numbers , Konno (2000) defines the hyperpolygon space , a hyperkähler analogue of the Kähler variety parametrizing polygons in with edge lengths . The polygon space can be interpreted as the moduli space of stable representations of a certain quiver with fixed dimension vector; from this point of view, is the hyperkähler quiver variety defined by Nakajima. A quiver variety admits a natural action, and the union of the precompact orbits is called the core. We study the components of the core of , interpreting each one as a moduli space of pairs of polygons in with certain properties. Konno gives a presentation of the cohomology ring of ; we extend this result by computing the equivariant cohomology ring, as well as the ordinary and equivariant cohomology rings of the core components.
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Additional Information
Megumi Harada
Affiliation:
Department of Mathematics, University of Toronto, Ontario, Canada M5S 3G3
Email:
megumi@math.toronto.edu
Nicholas Proudfoot
Affiliation:
Department of Mathematics, University of California, Berkeley, California 94720
Email:
proudf@math.berkeley.edu
DOI:
http://dx.doi.org/10.1090/S0002994704035226
PII:
S 00029947(04)035226
Keywords:
Hyperk\"ahler geometry,
polygon space,
quiver variety,
equivariant cohomology
Received by editor(s):
August 23, 2003
Received by editor(s) in revised form:
October 1, 2003
Published electronically:
September 23, 2004
Article copyright:
© Copyright 2004 American Mathematical Society
