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Quotients of toric varieties by actions of subtori

100%

Święcicka J.

Colloquium Mathematicum

1999

tom 82

nr 1

105-116

Let X be an algebraic toric variety with respect to an action of an algebraic torus S. Let Σ be the corresponding fan. The aim of this paper is to investigate open subsets of X with a good quotient by the (induced) action of a subtorus T ⊂ S. It turns out that it is enough to consider open S-invariant subsets of X with a good quotient by T. These subsets can be described by subfans of Σ. We give a description of such subfans and also a description of fans corresponding to quotient varieties. Moreover, we give conditions for a subfan to define an open subset with a complete quotient space.

Lie groupoids as generalized atlases

100%

Pradines J.

Open Mathematics

2004

tom 2

nr 5

624-662

Starting with some motivating examples (classical atlases for a manifold, space of leaves of a foliation, group orbits), we propose to view a Lie groupoid as a generalized atlas for the “virtual structure” of its orbit space, the equivalence between atlases being here the smooth Morita equivalence. This “structure” keeps memory of the isotropy groups and of the smoothness as well. To take the smoothness into account, we claim that we can go very far by retaining just a few formal properties of embeddings and surmersions, yielding a very polymorphous unifying theory. We suggest further developments.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Open Mathematics

1 Pradines J.

1 Święcicka J.

1 2004

1 1999

Wyniki wyszukiwania

Quotients of toric varieties by actions of subtori

Lie groupoids as generalized atlases