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Geometric invariant theory of linear systems
Mathematical Proceedings of the Cambridge Philosophical Society, 1983In considering the geometric invariant theory of linear systems (pencils, nets, …) of geometrical objects (quadrics, cubic curves, binary forms,…) there are several ways to apply the basic theory. The object of this note is to point out the equivalence of different approaches and to apply this remark to a number of special cases.
C. Wall
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Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration
SpringerBriefs in Mathematics, 2019This survey intends to present the basic notions of Geometric Invariant Theory (GIT) through its paradigmatic application in the construction of the moduli space of holomorphic vector bundles.
Alfonso Zamora Saiz +1 more
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Existence of Locally Maximally Entangled Quantum States via Geometric Invariant Theory
Annales de l'Institute Henri Poincare. Physique theorique, 2017We study a question which has natural interpretations both in quantum mechanics and in geometry. Let $$V_{1},\cdots , V_{n}$$V1,⋯,Vn be complex vector spaces of dimension $$d_{1},\ldots ,d_{n}$$d1,…,dn and let $$G= {\text {SL}}_{d_{1}} \times \cdots ...
J. Bryan, Z. Reichstein, M. Raamsdonk
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Geometric constitutive theory and frame invariance
International Journal of Non-Linear Mechanics, 2013Abstract The need for a proper geometric approach to constitutive theory in non-linear continuum mechanics (NLCM) is witnessed by lasting debates about basic questions concerning time-invariance, integrability, conservativeness and frame invariance.
Romano G., BARRETTA, RAFFAELE
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Cohomology pairings on singular quotients in geometric invariant theory
, 2001In this paper we shall give formulas for the pairings of intersection cohomology classes of complementary dimensions in the intersection cohomology of geometric invariant-theoretic quotients for which semistability is not necessarily the same as ...
L. Jeffrey, Y. Kiem, F. Kirwan, J. Woolf
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Weight Theory in Geometric Invariant Theory
2017In the previous chapter the emphasis was on studying closed orbits in reductive group actions on affine varieties. We saw that this was essentially the same as studying orbits under regular representations. In most examples that we considered the generic orbits were usually closed. In this chapter, we consider similar questions for projective varieties
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D. Mumford’s Geometric Invariant Theory
1995We recall some basic definitions and results from geometric invariant theory, all contained in the first two chapters of D. Mumford’s book [59]. For the statements which are used in this monograph, except for those coming from the theory of algebraic groups, such as the finiteness of the algebra of invariants under the action of a reductive group, we ...
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Geometric Invariant Theory on Hilbert Schemes
1995The Positivity Theorems 6.22 and 6.24 allow to apply the Stability Criterion 4.25 and the Ampleness Criterion 4.33 to the Hilbert schemes H constructed in 1.46 and 1.52 for the moduli functors C and 𝔐, respectively. We start by defining the action of the group G = Sl(l + 1, k) or G = Sl(l + 1, k) × Sl(m + 1, k) on H and by constructing G-linearized ...
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