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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$(W,R)$-matroids and thin Schubert-type cells attached to algebraic torus actions
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by Yi Hu
Proc. Amer. Math. Soc. 123 (1995), 2607-2617
DOI: https://doi.org/10.1090/S0002-9939-1995-1223514-1

Abstract:

Given a projective variety acted on by an algebraic torus, we introduce the notion of (W, R)-matroids using the fixed-point set W and the set R of equivalence classes of one-parameter subgroups. The (W, R)-matroids provide close links among the geometry of torus orbits and Schubert-type cells, the theory of momentum polyhedra, and the combinatorial geometries. On the way to establishing the main theme of the paper, we showed that there are only finitely many Bialynicki-Birula decompositions induced by infinitely many one-parameter subgroups.
References
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Bibliographic Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 2607-2617
  • MSC: Primary 14L30; Secondary 14M25, 52B40
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1223514-1
  • MathSciNet review: 1223514