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Geometric invariant theory for graded additive groups
Journal of AlgebraWe consider geometric invariant theory for \emph{graded additive groups}, groups of the form $\mathbb{G}_a^r\rtimes_w\mathbb{G}_m$ such that the $\mathbb{G}_m$-action on $\mathbb{G}_a^r$ is a scalar multiplication with weight $w\in\mathbb{N}_+$.
Yikun Qiao
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Master Spaces and the Coupling Principle:¶From Geometric Invariant Theory to Gauge Theory
Communications in Mathematical Physics, 1999 22 pagesInternational audienceWe introduce a general mathematical principle, with roots in Geometric Invariant Theory, which provides a unified way for understanding several celebrated results and conjectures like e. g.
Christian Okonek, Andrei Teleman
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A Geometric Approach for the Theory and Applications of 3D Projective Invariants
Journal of Mathematical Imaging and Vision, 2002zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Eduardo Bayro-Corrochano +1 more
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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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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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A Brief Introduction to Geometric Invariant Theory
2018We provide a brief introduction to Geometric Invariant Theory. Specifically, we discuss some foundational concepts and results and illustrate the general theory by way of examples.
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Geometric Invariant Theory, Holomorphic Vector Bundles and the Harder-Narasimhan Filtration
SpringerBriefs in Mathematics, 2021Alfonso Zamora, Ronald A Zúñiga-Rojas
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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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