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Group Actions and Invariant Theory
Edited by: A. Bialynicki-Birula, J. Carrell, P. Russell, and D. Snow
A co-publication of the AMS and Canadian Mathematical Society.
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Conference Proceedings, Canadian Mathematical Society
1989; 228 pp; softcover
Volume: 10
ISBN-10: 0-8218-6015-1
ISBN-13: 978-0-8218-6015-1
List Price: US$59
Member Price: US$47.20
Order Code: CMSAMS/10
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This volume contains the proceedings of a conference, sponsored by the Canadian Mathematical Society, on Group Actions and Invariant Theory, held in August, 1988 in Montreal. The conference was the third in a series bringing together researchers from North America and Europe (particularly Poland). The papers collected here will provide an overview of the state of the art of research in this area. The conference was primarily concerned with the geometric side of invariant theory, including explorations of the linearization problem for reductive group actions on affine spaces (with a counterexample given recently by J. Schwarz), spherical and complete symmetric varieties, reductive quotients, automorphisms of affine varieties, and homogeneous vector bundles.

Titles in this series are copublished with the Canadian Mathematical Society. Members of the Canadian Mathematical Society may order at the AMS member price.

Table of Contents

  • S. S. Abhyankar and S. B. Joshi -- Generalized codeletion and standard multitableaux
  • A. Bialynicki-Birula and J. Swiecicka -- On exotic orbit spaces of tori acting on projective varieties
  • M. Brion -- On spherical varieties of rank one
  • P. Blass, K. J. Horodam, P. B. Kleidman, and A. J. E. Ryba -- A new doubly-infinite class of factorial rings
  • A. Fauntleroy -- .I.T. for general algebraic groups
  • F. D. Grosshans -- Finitely generated rings of invariants having rational singularities
  • J. Horvath -- Bruhat decomposition in unipotent actions
  • J. Jurkiewicz -- On some reductive group actions on affine space
  • J. Konarski -- Some examples of cohomological projective spaces, via \(\mathbb{C}^+\)-actions
  • G. R. Kempf -- Equations of isotropy
  • M. Koras and P. Russell -- n linearizing "Good" \(\mathbb{C}^\ast\)-actions on \(\mathbb{C}^3\)
  • M. Koras and P. Russell -- Codimension \(2\) torus actions on affine \(n\)-space
  • H. Kraft -- \(G\)-vector bundles and the linearization problem
  • H. Kraft and G. W. Schwarz -- Reductive group actions on affine space with one-dimensional quotient
  • A. Magid -- Equivariant completions and tensor products
  • T. Nakano -- Regular actions of semisimple algebraic groups on projective threefolds, especially \(SL(2)\)
  • V. L. Popov -- Some applications of algebra of functions on \(G/U\)
  • M. S. Putcha -- Linear algebraic monoids and \(G/H\) embeddings
  • L. E. Renner -- Reductive embeddings
  • D. M. Snow -- Homogeneous vector bundles
  • L. Tan -- Some recent developments in the Popov-Pommerening conjecture
  • D. L. Wehlau -- Some recent results on the Popov conjecture
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