Results 1 to 10 of about 126 (101)
Unipotent group actions on affine varieties
Journal of Algebra, 2011 Algebraic actions of unipotent groups $U$ actions on affine $k-$varieties $X$ ($k$ an algebraically closed field of characteristic 0) for which the algebraic quotient $X//U$ has small dimension are considered$.$ In case $X$ is factorial, $O(X)^{\ast}=k^{\ast},$ and $X//U$ is one-dimensional, it is shown that $O(X)^{U}$=$k[f]$, and if some point in $X ...
Derksen, H. +3 more
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On the Cohomological Spectrum and Support Varieties for Infinitesimal Unipotent Supergroup Schemes [PDF]
Springer Proceedings in Mathematics and Statistics, 2019 We show that if $G$ is an infinitesimal elementary supergroup scheme of height $\leq r$, then the cohomological spectrum $|G|$ of $G$ is naturally homeomorphic to the variety $\mathcal{N}_r(G)$ of supergroup homomorphisms $ρ: \mathbb{M}_r \rightarrow G$ from a certain (non-algebraic) affine supergroup scheme $\mathbb{M}_r$ into $G$.
Christopher M Drupieski +1 more
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UNIPOTENT COMMUTATIVE GROUP ACTIONS ON FLAG VARIETIES AND NILPOTENT MULTIPLICATIONS [PDF]
Transformation Groups, 2015 25 pages, master thesis (improved afterwards)
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Radiant toric varieties and unipotent group actions
Bulletin Des Sciences Mathematiques27 ...
Ivan Arzhantsev +2 more
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Composition series for unipotent group varieties
Journal of Algebra, 1987 Let U be a unipotent group variety over an arbitrary field k. Let \(T\times U\to U\) be an action by group automorphisms of a torus T on U. Everything is defined over k. The author proves (in a very short way) the following theorem: If the action of T on the Lie algebra of U is diagonalizable over k, we have a T-invariant composition series defined ...
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Geometric crystals on flag varieties and unipotent subgroups of classical groups
Journal of Geometry and Physics, 2011 For a classical simple algebraic group $G$ we obtain the affirmative answer for the conjecture in [8] that there exists an isomorphism between the geometric crystal on the flag variety and the one on the unipotent subgroup $U^-$.
Toshiki Nakashima
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Toric varieties admitting an action of a unipotent group with a finite number of orbits
Research in Mathematical SciencesWe describe complete simplicial toric varieties on which a unipotent group acts with a finite number of orbits. We also provide a complete list of such varieties in the case where the dimension is equal to 2.
Anton Shafarevich
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The fixed point subvarieties of unipotent transformations on the flag varieties
Journal of the Mathematical Society of Japan, 1985 Let V be an n-dimensional vector space over a field K. For an ordered sequence \(\mu =(\mu_ 1,...,\mu_ s)\) of positive integers such that \(\mu_ 1+...+\mu_ s=n,\) let \(F_{\mu}=F_{\mu}(V)\) be the partial flag variety of type \(\mu\) defined by \(\{(W_ 1,...,W_{s-1})\in \prod_{1\leq i\leq s-1}G_{d_ i}(V);W_ i\subset W_{i+1}(1\leq i\leq s-2)\},\) where
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Hamiltonian actions of unipotent groups on compact K\"ahler manifolds [PDF]
Épijournal de Géométrie Algébrique, 2018 We study meromorphic actions of unipotent complex Lie groups on compact K\"ahler manifolds using moment map techniques. We introduce natural stability conditions and show that sets of semistable points are Zariski-open and admit geometric quotients that ...
Daniel Greb, Christian Miebach
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On Special Pieces in the Unipotent Variety [PDF]
Experimental Mathematics, 1999 This article is the result of experiments performed using computer programs written in the GAP language. We describe an algorithm which computes a set of rational functions attached to a finite Coxeter group W. Conjecturally, these rational functions should be polynomials, and in the case where W is the Weyl group of a Chevalley group G defined over Fq,
Geck, Meinolf, Malle, Gunter
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