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On symmetric semialgebraic sets and orbit spaces

Ludwig Bröcker (1998)

Banach Center Publications

For a symmetric (= invariant under the action of a compact Lie group G) semialgebraic basic set C, described by s polynomial inequalities, we show, that C can also be written by s + 1 G-invariant polynomials. We also describe orbit spaces for the action of G by a number of inequalities only depending on the structure of G.

On the geometry of moduli of curves and line bundles

Claudio Fontanari (2005)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Here we focus on the geometry of P ¯ d , g , the compactification of the universal Picard variety constructed by L. Caporaso. In particular, we show that the moduli space of spin curves constructed by M. Cornalba naturally injects into P ¯ d , g and we give generators and relations of the rational Picard group of P ¯ d , g , extending previous work by A. Kouvidakis.

On the motive of a quotient variety.

Sebastián del Baño Rollin, Vicente Navarro Aznar (1998)

Collectanea Mathematica

We show that the motive of the quotient of a scheme by a finite group coincides with the invariant submotive.

Optimal destabilizing vectors in some Gauge theoretical moduli problems

Laurent Bruasse (2006)

Annales de l’institut Fourier

We prove that the well-known Harder-Narsimhan filtration theory for bundles over a complex curve and the theory of optimal destabilizing 1 -parameter subgroups are the same thing when considered in the gauge theoretical framework.Indeed, the classical concepts of the GIT theory are still effective in this context and the Harder-Narasimhan filtration can be viewed as a limit object for the action of the gauge group, in the direction of an optimal destabilizing vector. This vector appears as an extremal...

Quantization of Drinfeld Zastava in type A

Michael Finkelberg, Leonid Rybnikov (2014)

Journal of the European Mathematical Society

Drinfeld Zastava is a certain closure of the moduli space of maps from the projective line to the Kashiwara flag scheme of the affine Lie algebra 𝔰𝔩 ^ n . We introduce an affine, reduced, irreducible, normal quiver variety Z which maps to the Zastava space bijectively at the level of complex points. The natural Poisson structure on the Zastava space can be described on Z in terms of Hamiltonian reduction of a certain Poisson subvariety of the dual space of a (nonsemisimple) Lie algebra. The quantum Hamiltonian...

Quotients of an affine variety by an action of a torus

Olga Chuvashova, Nikolay Pechenkin (2013)

Open Mathematics

Let X be an affine T-variety. We study two different quotients for the action of T on X: the toric Chow quotient X/C T and the toric Hilbert scheme H. We introduce a notion of the main component H 0 of H, which parameterizes general T-orbit closures in X and their flat limits. The main component U 0 of the universal family U over H is a preimage of H 0. We define an analogue of a universal family WX over the main component of X/C T. We show that the toric Chow morphism restricted on the main components...

Reductive group actions on affine varieties and their doubling

Dmitri I. Panyushev (1995)

Annales de l'institut Fourier

We study G -actions of the form ( G : X × X * ) , where X * is the dual (to X ) G -variety. These actions are called the doubled ones. A geometric interpretation of the complexity of the action ( G : X ) is given. It is shown that the doubled actions have a number of nice properties, if X is spherical or of complexity one.

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