On the moment measure conjecture

• Autorzy: Białynicki-Birula A.
• Języki publikacji: EN

Abstrakty

EN

The main purpose of the paper is to give a characterization of such open invariant subsets U of projective spaces with an action of a torus T, which admit a good quotient U --> U//T and the quotient space is compact. It follows from the result that moment measure conjecture (stated in [4]) is valid in the case of projective spaces (and their products).

Słowa kluczowe

EN

algebraic actions of tori; quotient spaces

PL

przestrzeń ilorazowa; geometria algebraiczna; algebra; topologia

• Wydawca: Instytut Matematyczny PAN
• Czasopismo: Bulletin of the Polish Academy of Sciences. Mathematics
• Rocznik: 2002
• Tom: Vol. 50, no 1
• Strony: 33--40
• Opis fizyczny: Bibliogr. 10 poz., rys.

Twórcy

autor

Białynicki-Birula A.

• Institute of Mathematics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland

Bibliografia

• [1] M. F. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc., 14 (1982) 1-15.
• [2] A. Białynicki-Birula, A. Sommese, Quotients by C* and SL(2) actions, Trans. Amer. Math. Soc., 279 (1983) 773-800.
• [3] A. Białynicki-Birula, A. Sommese, Quotients by C* X C* actions, Trans. Amer. Math. Soc., 279 (1983) 773-800.
• [4] A. Białynicki-Birula, A. Sommese, A conjecture about quotients by tori, Adv. Stud. Pure Math., 8 (1986) 59-68.
• [5] A. Białynicki-Birula, J. Święcicka, Complete quotients by algebraic torus actions, in: Group actions and vector fields, Lecture Notes in Math., 956, Springer-Verlag, Berlin Heidelberg New York (1982) 10-22.
• [6] A. Białynicki-Birula, J. Święcicka, Open subsets of projective spaces with a good quotient by an action of a reductive group, Transform. Groups, 1 (1996) 153-185.
• [7] D. Gross, Compact quotients by C*-actions, Pacific J. Math., 114 (1984) 149-164.
• [8] Y i Hu, (W, R)-matroids and thin Schubert-type cells attached to algebraic torus actions, Proc. Amer. Math. Soc., 123 (1995) 2607-2617.
• [9] H. Sumihiro, Equivariant completions, J. Math. Kyoto Univ., 14 (1974) 1-28.
• [10] G. Kempf, F. Knudsen, D. Mumford, B. Saint-Donat, Toroidal embeddings I, Lecture Notes in Math., 339, Springer-Verlag, Berlin Heidelberg New York 1973.