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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Quotients by $ {\bf C}\sp{\ast} $ and $ {\rm SL}(2,{\bf C})$ actions


Authors: Andrzej Białynicki-Birula and Andrew John Sommese
Journal: Trans. Amer. Math. Soc. 279 (1983), 773-800
MSC: Primary 32M99; Secondary 14L30
DOI: https://doi.org/10.1090/S0002-9947-1983-0709583-X
MathSciNet review: 709583
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Abstract: Let $ \rho :{{\mathbf{C}}^{\ast}} \times X \to X$ be a meromorphic action of $ {{\mathbf{C}}^{\ast}}$ on a compact normal analytic space. We completely classify $ {{\mathbf{C}}^{\ast}}$-invariant open $ U \subseteq X$ with a compact analytic space $ U/T$ as a geometric quotient for a wide variety of actions, including all algebraic actions. As one application, we settle affirmatively a conjecture of D. Mumford on compact geometric quotients by $ {\text{SL(2}},{\mathbf{C}})$ of Zariski open sets of $ {({\mathbf{P}}_{\mathbf{C}}^1)^n}$.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0709583-X
Article copyright: © Copyright 1983 American Mathematical Society