Displaying similar documents to “Challenging problems on affine n -space”

On orbits of the automorphism group on an affine toric variety

Ivan Arzhantsev, Ivan Bazhov (2013)

Open Mathematics

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Let X be an affine toric variety. The total coordinates on X provide a canonical presentation X ¯ → X of X as a quotient of a vector space X ¯ by a linear action of a quasitorus. We prove that the orbits of the connected component of the automorphism group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.

Equidimensional actions of algebraic tori

Haruhisa Nakajima (1995)

Annales de l'institut Fourier

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Let X be an affine conical factorial variety over an algebraically closed field of characteristic zero. We consider equidimensional and stable algebraic actions of an algebraic torus on X compatible with the conical structure. We show that such actions are cofree and the nullcones of X associated with them are complete intersections.

Affine braid group actions on derived categories of Springer resolutions

Roman Bezrukavnikov, Simon Riche (2012)

Annales scientifiques de l'École Normale Supérieure

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In this paper we construct and study an action of the affine braid group associated with a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the Springer resolution of the nilpotent cone. In particular, we describe explicitly the action of the Artin braid group. This action is a “categorical version” of Kazhdan-Lusztig-Ginzburg’s construction of the affine Hecke algebra, and is used in particular by the first author and I. Mirković...