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Stability conditions in geometric invariant theory [PDF]
The Quarterly Journal of Mathematics, 2022 We explain how structures analogous to those appearing in the theory of stability conditions on abelian and triangulated categories arise in geometric invariant theory.
R. Dervan, Andrés Ibáñez núñez
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Geometric invariant theory and the generalized eigenvalue problem [PDF]
Annales de l'Institut Fourier, 2007 Let G be a connected reductive subgroup of a complex connected reductive group $\hat{G}$. Fix maximal tori and Borel subgroups of G and ${\hat{G}}$. Consider the cone $\mathcal{LR}(G,{\hat{G}})$ generated by the pairs $(\nu,{\hat{\nu}})$ of dominant ...
N. Ressayre
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Towards non-reductive geometric invariant theory [PDF]
Pure and Applied Mathematics Quarterly, 2007 We study linear actions of algebraic groups on smooth projective varieties X. A guiding goal for us is to understand the cohomology of "quotients" under such actions, by generalizing (from reductive to non-reductive group actions) existing methods ...
Doran, Brent, Kirwan, Frances
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Gauge Invariant Geometric Variables For Yang-Mills Theory [PDF]
Nuclear Physics B, 1995 In a previous publication [1], local gauge invariant geometric variables were introduced to describe the physical Hilbert space of Yang-Mills theory. In these variables, the electric energy involves the inverse of an operator which can generically have ...
Bauer +21 more
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Geometric Invariant Theory [PDF]
SpringerBriefs in Mathematics, 2021 The purpose of Geometric Invariant Theory (abbreviated GIT) is to provide a way to define a quotient of an algebraic variety X by the action of a reductive complex algebraic group G with an algebro-geometric structure. In this chapter we present a sketch of the treatment with a variety of examples.
Alfonso Zamora Saiz +1 more
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An analytic application of Geometric Invariant Theory [PDF]
Journal of Geometry and Physics, 2020 Given a compact Kahler manifold, Geometric Invariant Theory is applied to construct analytic GIT-quotients that are local models for a classifying space of (poly)stable holomorphic vector bundles containing the coarse moduli space of stable bundles as an
N. Buchdahl, G. Schumacher
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Real Geometric Invariant Theory [PDF]
Differential Geometry in the Large, 2017 For linear actions of real reductive Lie groups we prove the Kempf-Ness Theorem about closed orbits and the Kirwan-Ness Stratification Theorem of the null cone. Since our completely self-contained proof focuses strongly on geometric and analytic methods,
Christoph Bohm, Ramiro A. Lafuente
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Relative geometric invariant theory
L’Enseignement Mathématique, 2021 Relative geometric invariant theory is an invariant theory for equivariant projective morphisms between algebraic varieties endowed with an action of a reductive linear algebraic group. We will give brief accounts of the basic results of relative geometric invariant theory and present alternative proofs for recent results obtained by Halle, Hulek, and ...
A. Schmitt
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Geometric invariant theory and Einstein–Weyl geometry [PDF]
Expositiones Mathematicae, 2011 In this article, we give a survey of Geometric Invariant Theory for Toric Varieties, and present an application to the Einstein-Weyl Geometry. We compute the image of the Minitwistor space of the Honda metrics as a categorical quotient according to the most efficient linearization. The result is the complex weighted projective space CP_(1,1,2). We also
Mustafa Kalafat
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Geometric Invariant Theory based on Weil Divisors [PDF]
Compositio Mathematica, 2003 Given an action of a reductive group on a normal variety, we construct all invariant open subsets admitting a good quotient with a quasiprojective or a divisorial quotient space. Our approach extends known constructions like Mumford's Geometric Invariant
Jürgen Hausen +3 more
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