Group Actions and Invariant Theory: Proceedings of the 1988 Montreal Conference, Held August 1-6, 1988

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American Mathematical Soc., 1989 - 228 Seiten
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.
 

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Inhalt

GENERALIZED CODELETION AND STANDARD MULTITABLEAUX
1
ON EXOTIC ORBIT SPACES OF TORI ACTING ON PROJECTIVE VARIETIES
25
ON SPHERICAL VARIETIES OF RANK ONE
31
A NEW DOUBLYINFINITE CLASS OF FACTORIAL RINGS
43
GIT FOR GENERAL ALGEBRAIC GROUPS
45
FINITELY GENERATED RINGS OF INVARIANTS HAVING RATIONAL SINGULARITIES
53
BRUHAT DECOMPOSITION IN UNIPOTENT ACTIONS
61
ON SOME REDUCTIVE GROUP ACTIONS ON AFFINE SPACE
67
𝐺VECTOR BUNDLES AND THE LINEARIZATION PROBLEM
111
REDUCTIVE GROUP ACTIONS ON AFFINE SPACE WITH ONEDIMENSIONAL QUOTIENT
125
EQUIVARIANT COMPLETIONS AND TENSOR PRODUCTS
133
REGULAR ACTIONS OF SEMISIMPLE ALGEBRAIC GROUPS ON PROJECTIVE THREEFOLDS ESPECIALLY 𝑆𝐿2
137
SOME APPLICATIONS OF ALGEBRA OF FUNCTIONS ON 𝐺𝑈
157
LINEAR ALGEBRAIC MONOIDS AND 𝐺𝐻 EMBEDDINGS
167
REDUCTIVE EMBEDDINGS
175
HOMOGENEOUS VECTOR BUNDLES
193

SOME EXAMPLES OF COHOMOLOGICAL PROJECTIVE SPACES VIA CACTIONS
73
EQUATIONS OF ISOTROPY
85
ON LINEARIZING GOOD CACTIONS ON C³
93
CODIMENSION 2 TORUS ACTIONS ON AFFINE 𝑛SPACE
103
SOME RECENT DEVELOPMENTS IN THE POPOVPOMMERENING CONJECTURE
207
SOME RECENT RESULTS ON THE POPOV CONJECTURE
221
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