scholarly journals A fixed point formula of Lefschetz type in Arakelov geometry III: representations of Chevalley schemes and heights of flag varieties

2002 ◽  
Vol 147 (3) ◽  
pp. 633-669 ◽  
Author(s):  
Christian Kaiser ◽  
Kai Köhler
Keyword(s):  
Fixed Point ◽  
Flag Varieties ◽  
Lefschetz Type ◽  
Arakelov Geometry

scholarly journals A fixed point formula of Lefschetz type in Arakelov geometry I: statement and proof

2001 ◽  
Vol 145 (2) ◽  
pp. 333-396 ◽  
Author(s):  
Kai Köhler ◽  
Damian Roessler
Keyword(s):  
Fixed Point ◽  
Lefschetz Type ◽  
Arakelov Geometry

scholarly journals A fixed point formula of Lefschetz type in Arakelov geometry II: A residue formula

2002 ◽  
Vol 52 (1) ◽  
pp. 81-103 ◽  
Author(s):  
Kai Köhler ◽  
Damien Roessler
Keyword(s):  
Fixed Point ◽  
Residue Formula ◽  
Lefschetz Type ◽  
Arakelov Geometry

scholarly journals A Lefschetz-type fixed point theorem

1975 ◽  
Vol 88 (2) ◽  
pp. 103-115 ◽  
Author(s):  
L. Górniewicz
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Lefschetz Type

scholarly journals A FILTRATION ON EQUIVARIANT BOREL–MOORE HOMOLOGY

2019 ◽  
Vol 7 ◽  
Author(s):  
ARAM BINGHAM ◽  
MAHIR BILEN CAN ◽  
YILDIRAY OZAN
Keyword(s):  
Fixed Point ◽  
Maximal Torus ◽  
Flag Varieties ◽  
Direct Sum ◽  
Equivariant Embedding ◽  
Graded Module ◽  
Homogeneous Variety

Let $G/H$ be a homogeneous variety and let $X$ be a $G$ -equivariant embedding of $G/H$ such that the number of $G$ -orbits in $X$ is finite. We show that the equivariant Borel–Moore homology of $X$ has a filtration with associated graded module the direct sum of the equivariant Borel–Moore homologies of the $G$ -orbits. If $T$ is a maximal torus of $G$ such that each $G$ -orbit has a $T$ -fixed point, then the equivariant filtration descends to give a filtration on the ordinary Borel–Moore homology of $X$ . We apply our findings to certain wonderful compactifications as well as to double flag varieties.

On Orbit Closures of Symmetric Subgroups in Flag Varieties

2000 ◽  
Vol 52 (2) ◽  
pp. 265-292 ◽  
Author(s):  
Michel Brion ◽  
Aloysius G. Helminck
Keyword(s):  
Fixed Point ◽  
Borel Subgroup ◽  
Reductive Group ◽  
Double Coset ◽  
Restriction Map ◽  
Flag Varieties ◽  
Parabolic Subgroups ◽  
Involutive Automorphism ◽  
Orbit Closures ◽  
Geometric Analogue

AbstractWe study K-orbits in G/P where G is a complex connected reductive group, P ⊆ G is a parabolic subgroup, and K ⊆ G is the fixed point subgroup of an involutive automorphism θ. Generalizing work of Springer, we parametrize the (finite) orbit set K \ G/P and we determine the isotropy groups. As a consequence, we describe the closed (resp. affine) orbits in terms of θ-stable (resp. θ-split) parabolic subgroups. We also describe the decomposition of any (K, P)-double coset in G into (K, B)-double cosets, where B ⊆ P is a Borel subgroup. Finally, for certain K-orbit closures X ⊆ G/B, and for any homogeneous line bundle on G/B having nonzero global sections, we show that the restriction map resX : H0(G/B, ) → H0(X, ) is surjective and that Hi(X, ) = 0 for i ≥ 1. Moreover, we describe the K-module H0(X, ). This gives information on the restriction to K of the simple G-module H0(G/B, ). Our construction is a geometric analogue of Vogan and Sepanski’s approach to extremal K-types.

scholarly journals Goresky–MacPherson Calculus for the Affine Flag Varieties

2010 ◽  
Vol 62 (2) ◽  
pp. 473-480 ◽  
Author(s):  
Zhiwei Yun
Keyword(s):  
Fixed Point ◽  
Equivariant Cohomology ◽  
Flag Variety ◽  
Moment Map ◽  
Flag Varieties ◽  
The Moment ◽  
Affine Flag Variety ◽  
Affine Flag

AbstractWe use the fixed point arrangement technique developed by Goresky and MacPherson to calculate the part of the equivariant cohomology of the affine flag variety ℱ ℓ G generated by degree 2. We use this result to show that the vertices of the moment map image of ℱ ℓ G lie on a paraboloid.

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