scholarly journals Corrigendum to “Orbit closures in the enhanced nilpotent cone” [Adv. Math. 219 (1) (2008) 27–62]

2011 ◽  
Vol 228 (5) ◽  
pp. 2984-2988 ◽  
Author(s):  
Pramod N. Achar ◽  
Anthony Henderson
Keyword(s):  
Nilpotent Cone ◽  
Orbit Closures

scholarly journals Normality of orbit closures in the enhanced nilpotent cone

2011 ◽  
Vol 203 ◽  
pp. 1-45 ◽  
Author(s):  
Pramod N. Achar ◽  
Anthony Henderson ◽  
Benjamin F. Jones
Keyword(s):  
Nilpotent Orbit ◽  
Complete Intersections ◽  
Quiver Variety ◽  
Quiver Varieties ◽  
Nilpotent Cone ◽  
Orbit Closures ◽  
Special Cases

AbstractWe continue the study of the closures of GL(V)-orbits in the enhanced nilpotent cone V × N begun by the first two authors. 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.

scholarly journals Normality of orbit closures in the enhanced nilpotent cone

2011 ◽  
Vol 203 ◽  
pp. 1-45 ◽  
Author(s):  
Pramod N. Achar ◽  
Anthony Henderson ◽  
Benjamin F. Jones
Keyword(s):  
Nilpotent Orbit ◽  
Complete Intersections ◽  
Quiver Variety ◽  
Quiver Varieties ◽  
Nilpotent Cone ◽  
Orbit Closures ◽  
Special Cases

AbstractWe continue the study of the closures of GL(V)-orbits in the enhanced nilpotent coneV × Nbegun by the first two authors. 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.

scholarly journals Orbit closures in the enhanced nilpotent cone

2008 ◽  
Vol 219 (1) ◽  
pp. 27-62 ◽  
Author(s):  
Pramod N. Achar ◽  
Anthony Henderson
Keyword(s):  
Nilpotent Cone ◽  
Orbit Closures

scholarly journals Homogeneous orbit closures and applications

2011 ◽  
Vol 32 (2) ◽  
pp. 785-807 ◽  
Author(s):  
ELON LINDENSTRAUSS ◽  
URI SHAPIRA
Keyword(s):  
Real Number ◽  
Unit Volume ◽  
Orbit Closures ◽  
Image Position

AbstractWe give new classes of examples of orbits of the diagonal group in the space of unit volume lattices in ℝd for d≥3 with nice (homogeneous) orbit closures, as well as examples of orbits with explicitly computable but irregular orbit closures. We give Diophantine applications to the former; for instance, we show that, for all γ,δ∈ℝ, where 〈c〉 denotes the distance of a real number c to the integers.

Classification of higher rank orbit closures in ${\mathcal H^{\mathrm{odd}}(4)}$

2016 ◽  
Vol 18 (8) ◽  
pp. 1855-1872 ◽  
Author(s):  
David Aulicino ◽  
Duc-Manh Nguyen ◽  
Alex Wright
Keyword(s):  
Orbit Closures ◽  
Higher Rank

scholarly journals Poincaré polynomials of generic torus orbit closures in Schubert varieties

2021 ◽  
pp. 189-208
Author(s):  
Eunjeong Lee ◽  
Mikiya Masuda ◽  
Seonjeong Park ◽  
Jongbaek Song
Keyword(s):  
Schubert Variety ◽  
Flag Variety ◽  
Schubert Varieties ◽  
Orbit Closure ◽  
Poincaré Polynomial ◽  
Content Type ◽  
Eulerian Polynomial ◽  
Orbit Closures

The closure of a generic torus orbit in the flag variety G / B G/B of type  A A is known to be a permutohedral variety, and its Poincaré polynomial agrees with the Eulerian polynomial. In this paper, we study the Poincaré polynomial of a generic torus orbit closure in a Schubert variety in  G / B G/B . When the generic torus orbit closure in a Schubert variety is smooth, its Poincaré polynomial is known to agree with a certain generalization of the Eulerian polynomial. We extend this result to an arbitrary generic torus orbit closure which is not necessarily smooth.

scholarly journals The Smooth Torus Orbit Closures in the Grassmannians

2019 ◽  
Vol 305 (1) ◽  
pp. 251-261
Author(s):  
Masashi Noji ◽  
Kazuaki Ogiwara
Keyword(s):  
Orbit Closures
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