Global Sections of Line Bundles on a Wonderful Compactification of the General Linear Group
نویسنده
چکیده
In a previous paper [K1] I have constructed a compactification KGLn of the general linear group GLn, which in many respects is analogous to the so called wonderful compactification of adjoint semisimple algebraic groups as studied by De Concini and Procesi. In particular there is an action of G = GLn × GLn on this compactification. In this paper we show how the space of global section of an arbitrary G-linearized line bundle on KGLn and its orbit-closures decomposes into a direct sum of simple G-modules.
منابع مشابه
Construction of Equivariant Vector Bundles
Let X be the wonderful compactification of a complex adjoint symmetric space G/K such that rk(G/K) = rk(G) − rk(K). We show how to extend equivariant vector bundles on G/K to equivariant vector bundles on X , generated by their global sections and having trivial higher cohomology groups. This relies on a geometric construction of equivariant vector bundles in the setting of varieties with reduc...
متن کاملCompactification of the Symplectic Group via Generalized Symplectic Isomorphisms
Let G be a connected reductive algebraic group over an algebraically closed field k of characteristic zero. We have a left (G×G)-action on G defined as (g1, g2) ·x := g1xg −1 2 . A (G×G)-equivariant embedding G ↪→ X is said to be regular (cf. [BDP], [Br, §1.4]) if the following conditions are satisfied: (i) X is smooth and the complement X \G is a normal crossing divisor D1 ∪ · · · ∪Dn. (ii) Ea...
متن کاملProjective Normality of Model Varieties and Related Results
We prove that the multiplication of sections of globally generated line bundles on a model wonderful varietyM of simply connected type is always surjective. This follows by a general argument which works for every wonderful variety and reduces the study of the surjectivity for every couple of globally generated line bundles to a finite number of cases. As a consequence, the cone defined by a co...
متن کاملEquivariant vector bundles on group completions
In this paper, we describe the category of bi-equivariant vector bundles on a bi-equivariant smooth (partial) compactification of a reductive algebraic group with normal crossing boundary divisors. Our result is a generalization of the description of the category of equivariant vector bundles on toric varieties established by A. As an application, we prove splitting of equivariant vector bundle...
متن کاملThe Moduli Stack of Gieseker-sl2-bundles on a Nodal Curve Ii
Let X0 be an irreducible projective nodal curve with only one singular point, and let P0 be a line bundle on X0. The moduli SUX0(r;P0) of rank r vector bundles on X0 with determinant P0 is not compact. In [A], using the technique of Kausz ([K1], [K2]), we constructed a compactification GSL2B(X0;P0) of SUX0(2;P0), and studied its structure. Surprisingly, despite its seemingly natural definition,...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2004