scholarly journals A classification of $H$-primes of quantum partial flag varieties

2010 ◽  
Vol 138 (04) ◽  
pp. 1249-1249 ◽  
Author(s):  
Milen Yakimov
Keyword(s):  
Flag Varieties ◽  
Partial Flag Varieties

scholarly journals Moduli of toric vector bundles

2008 ◽  
Vol 144 (5) ◽  
pp. 1199-1213 ◽  
Author(s):  
Sam Payne
Keyword(s):  
Linear Group ◽  
Group Action ◽  
Chern Class ◽  
Vector Bundles ◽  
Closed Subscheme ◽  
Flag Varieties ◽  
Moduli Stack ◽  
Rank Conditions ◽  
Partial Flag Varieties

AbstractWe give a presentation of the moduli stack of toric vector bundles with fixed equivariant total Chern class as a quotient of a fine moduli scheme of framed bundles by a linear group action. This fine moduli scheme is described explicitly as a locally closed subscheme of a product of partial flag varieties cut out by combinatorially specified rank conditions. We use this description to show that the moduli of rank three toric vector bundles satisfy Murphy’s law, in the sense of Vakil. The preliminary sections of the paper give a self-contained introduction to Klyachko’s classification of toric vector bundles.

scholarly journals Some results on equivariant contact geometry for partial flag varieties

2016 ◽  
Vol 27 (08) ◽  
pp. 1650066 ◽  
Author(s):  
Peter Crooks ◽  
Steven Rayan
Keyword(s):  
Vector Bundles ◽  
Contact Structures ◽  
Flag Varieties ◽  
Contact Manifolds ◽  
Projective Varieties ◽  
Simply Connected ◽  
Complex Projective ◽  
Special Case ◽  
Partial Flag Varieties

We study equivariant contact structures on complex projective varieties arising as partial flag varieties [Formula: see text], where [Formula: see text] is a connected, simply-connected complex simple group of type ADE and [Formula: see text] is a parabolic subgroup. We prove a special case of the LeBrun-Salamon conjecture for partial flag varieties of these types. The result can be deduced from Boothby’s classification of compact simply-connected complex contact manifolds with transitive action by contact automorphisms, but our proof is completely independent and relies on properties of [Formula: see text]-equivariant vector bundles on [Formula: see text]. A byproduct of our argument is a canonical, global description of the unique [Formula: see text]-invariant contact structure on the isotropic Grassmannian of 2-planes in [Formula: see text].

scholarly journals Braiding via geometric Lie algebra actions

2012 ◽  
Vol 148 (2) ◽  
pp. 464-506 ◽  
Author(s):  
Sabin Cautis ◽  
Joel Kamnitzer
Keyword(s):  
Lie Algebra ◽  
Braid Group ◽  
Group Actions ◽  
Derived Categories ◽  
Flag Varieties ◽  
Coherent Sheaves ◽  
Cotangent Bundles ◽  
Partial Flag Varieties

AbstractWe introduce the idea of a geometric categorical Lie algebra action on derived categories of coherent sheaves. The main result is that such an action induces an action of the braid group associated to the Lie algebra. The same proof shows that strong categorical actions in the sense of Khovanov–Lauda and Rouquier also lead to braid group actions. As an example, we construct an action of Artin’s braid group on derived categories of coherent sheaves on cotangent bundles to partial flag varieties.

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