In this article, we prove that a -homology plane with two algebraically independent -actions is isomorphic to either the affine plane or a quotient of an affine hypersurface in the affine -space via a free -action, where is the order of a finite group .
Two geometric interpretations of the bar automorphism in the positive part of a quantized enveloping algebra are given. The first is in terms of numbers of rational points over finite fields of quiver analogues of orbital varieties; the second is in terms of a duality of constructible functions provided by preprojective varieties of quivers.
In this paper we compute the integral Chow ring of the stack of smooth uniform cyclic covers of the projective line and we give explicit generators.
A rational map ϕ: ℙ¹ → ℙ¹ along with an ordered list of fixed and critical points is called a totally marked rational map. The space of totally marked degree two rational maps can be parametrized by an affine open subset of (ℙ¹)⁵. We consider the natural action of SL₂ on induced from the action of SL₂ on (ℙ¹)⁵ and prove that the quotient space exists as a scheme. The quotient is isomorphic to a Del Pezzo surface with the isomorphism being defined over ℤ[1/2].