Commentarii Mathematici Helvetici
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Published online: 2009-12-23
Some topological properties of quotients modulo semisimple algebraic groupsR. V. Gurjar (1) Tata Institute of Fundamental Research, Bombay, India
We will prove a general result in Invariant Theory, viz. for a quotient ℂn//G, where G is a connected complex semisimple algebraic group, the local first homology group at any point in the quotient ℂn//G is trivial and the local second homology group is finite. Using this we will prove that the completion of the local ring of any point in ℂn//G is a unique factorization domain (UFD).
Keywords: Semisimple algebraic group, quotient, homology group
Gurjar R.: Some topological properties of quotients modulo semisimple algebraic groups. Comment. Math. Helv. 84 (2009), 793-806. doi: 10.4171/CMH/181