Normality of orbit closure

Author: wiuu

August undefined, 2024

WebLexX be the closure of aG-orbit in the Lie algebra of a connected reductive groupG. It seems that the varietyX is always normal. After a reduction to nilpotent orbits, this is proved for some special cases. Results on determinantal schemes are used forGl n . IfX is small enough we use a resolution and Bott's theorem on the cohomology of homogeneous … Web1 de dez. de 2015 · In this note we investigate the normality of closures of orthogonal and symplectic nilpotent orbits in positive characteristic. We prove that the closure of such a …

Normality of orbit closures in the enhanced nilpotent cone

WebLet N be a quiver representation with non-zero admissible annihilator. In this paper, we prove the normality of the orbit closure ŌN$\\bar {\\mathcal {O}}_{N}$ when it is a hypersurface. The result thus gives new examples of normal orbit closures of quiver representations. Web1 de jan. de 2015 · Download PDF Abstract: In this note we investigate the normality of closures of orthogonal and symplectic nilpotent orbits in positive characteristic. We prove … chirps definition

On the normality of orbit closures which are hypersurfaces

Web3 de fev. de 2016 · Let N be a quiver representation with non-zero admissible annihilator. In this paper, we prove the normality of the orbit closure O ̄ N $\\bar {\\mathcal {O}}_{N}$ when it is a hypersurface. The result thus gives new examples of normal orbit closures … WebNORMALITY OF ORBIT CLOSURES 5 A bipartition of size n is simply an ordered pair (μ;ν) of partitions with μ + ν =n.We put Q n ={bipartitions of size n}. Given a bipartition … WebWe recall the dimension formula for the orbit Cλ from [10, Remark 8]: dimCλ = 1 2 n2 − t i=1 λ2 i.(2) As the nilpotent cone of p(V) is G(V)-stable with only finitely many orbits, we have that orbit closure Cλ is G(V)-stable, and the complement Cλ \Cλ is a disjoint union of finitely many orbits. The relation Cμ ⊆ Cλ produces a ... chirp sdr

rt.representation theory - the affine coordinate ring of orbit closures ...

Normality of orbit closures for Dynkin quivers¶of type ?n

WebarXiv:1004.3822v1 [math.RT] 22 Apr 2010 NORMALITY OF ORBIT CLOSURES IN THE ENHANCED NILPOTENT CONE PRAMOD N. ACHAR, ANTHONY HENDERSON, AND … Web29 de out. de 2003 · For a non-generic torus orbit closure Y of G/B, one can find the corresponding fan using the Orbit-Cone correspondence. It should be noted that Y is not … graphing linear functions 8.16Web21 de abr. de 2010 · Normality of orbit closures in the enhanced nilpotent cone. April 2010; Nagoya Mathematical ... We prove that each closure is an invariant-theoretic quotient of … chirps downloaded audio books

"WebGEOMETRY OF ORBIT CLOSURES FOR E6, F4, G2 5 Let (Xn,αk) be one of the representations on our list.It deﬁnes the grading g= ⊕i∈Zgi where gi is the span of the roots which, written as a combination of simple roots, have αk with coeﬃcient i. The component g0 contains in addition a Cartan subal- gebra. G0 denotes the connected … " - Normality of orbit closure

Normality of orbit closure

Web22 de abr. de 2010 · We prove that each closure is an invariant-theoretic quotient of a suitably-defined enhanced quiver variety. We conjecture, and prove in special cases, that these enhanced quiver varieties are normal complete intersections, implying that the enhanced nilpotent orbit closures are also normal. WebAs a consequence, we obtain the normality of certain orbit closures of type E. 1 Introduction. Let K be a field of characteristic zero. A quiver is a pair Q=(Q 0,Q 1) where Q 0 is a set of vertices and Q 1 is a set of arrows. ... In the case of Dynkin quivers, the variety Y =q(Z(Q,β⊂β+γ)) is an orbit closure: Z(Q, ...

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Web1 de nov. de 2000 · Abstract The purpose of this note is to classify the torus orbit closures in an arbitrary algebraic homogeneous space G / P that are ... {Normality of Torus Orbit … Web10 de mar. de 2024 · We study closures of conjugacy classes in the symmetric matrices of the orthogonal group and we determine which one are normal varieties. In contrast to the result for the symplectic group where all classes have normal closure, there is only a relatively small portion of classes with normal closure. We perform a combinatorial …

WebIt is known that the orbit closures for the representations of the equioriented Dynkin quivers ? n are normal and Cohen–Macaulay varieties with rational singularities. In the paper we … WebMy second question, is the same but for the orbit closure of an orbit in the enhanced nilpotent cone (see, for instance, ... For algebraic properties of these coordinate rings like normality, Gorensteinness, rational singularities, see the book.

WebCanad. J. Math. Vol. 64 (6), 2012 pp. 1222–1247 http://dx.doi.org/10.4153/CJM-2012-012-7 Canadian Mathematical Society 2012c Normality of Maximal Orbit Closures for ...

WebB. Then GV ˆg (the G-saturation of V) is the closure of a nilpotent orbit O. As explained in [15], the normality of the full nilpotent cone implies that if the induced map C[G Bu] !C[G …

WebEDIT: Here I'm using shorthand to avoid normality questions: ... As Fu notes in Prop. 3.16, it follows from the main theorem of the paper that a nilpotent orbit whose closure admits … graphing linear equations with 3 variablesWeb24 de jul. de 2024 · It is easily checked that this \mathbf {C}^* -action has only positive weights and \tilde {O} becomes a conical symplectic variety. It may happen that \tilde {O} coincides with a normal nilpotent orbit closure of a different complex semisimple Lie algebra (cf. [ 3, Example 3.5]). In such a case the maximal weight is 1. chirps cricket flour chipsWebbe the closure of the orbit of;c f. Then the \-cycle C— CΊ 4- ••• -f C s is Q-homologous to zero in X. 2) Suppose that G = C. Let C be a closure of some orbit such that either C is singular or (C is nonsingular but) the intersection of C with XG is not transversal. Then C is Q-homomologous to zero in X. graphing linear functions calculatorWebThe normality of the orbit closure ON in the case (C) of Theorem 1.2 is an open question in general, and we shall handle it in a separated paper. Since ON is an irreducible aﬃne hypersurface, then, by a well-known criterion of Serre (see, for example, [7, III.8]), its normality is equivalent to graphing linear functions by plotting pointsWeb10 de mar. de 2024 · We study closures of conjugacy classes in the symmetric matrices of the orthogonal group and we determine which one are normal varieties. In contrast to the … graphing linear equations y 2xWebIt is trivial to check by this condition that the simple harmonic oscillator takes two circuits for a closed orbit and the Kepler potential only one. This latter is true of any negative … graphing linear functions khan academyWebity of the orbit closure O¯N in the case (C) of Theorem 1.2 is an open question in general, and we shall handle it in a separate paper. Since O¯N is an irreducible afﬁne hypersurface, then, by a well-known criterion of Serre (see, for example, section III.8 of [7]), its normality is equivalent to the non-singularity graphing linear equations y 3x-2