Infinite Grassmannians and Moduli Spaces of G–bundles
نویسندگان
چکیده
Introduction. These are notes for my eight lectures given at the C.I.M.E. session on “Vector bundles on curves. New directions” held at Cetraro (Italy) in June 1995. The work presented here was done in collaboration with M.S. Narasimhan and A. Ramanathan and appeared in [KNR]. These notes differ from [KNR] in that we have added three appendices (A)-(C) containing basic definitions and results (we need) on ind-varieties, Kac-Moody Lie algebras, the associated groups and their flag varieties. We also have modified the proof (given in §7) of basic extension result (Proposition 6.5), and we hope that it is more transparent than the one given in [KNR, §7]. We now describe the main result of this note. Let C be a smooth projective irreducible algebraic curve over C of any genus and G a connected simply-connected simple affine algebraic group over C. In this note we elucidate the relationship between
منابع مشابه
Framed Moduli and Grassmannians of Submodules
In this work we study a realization of moduli spaces of framed quiver representations as Grassmannians of submodules devised by Markus Reineke. Obtained is a generalization of this construction to finite dimensional associative algebras and for quivers with oriented cycles over an arbitrary infinite field. As an application we get an explicit realization of fibers for the moduli space bundle ov...
متن کاملDrinfeld Moduli Schemes and Infinite Grassmannians
The aim of this paper is to construct an immersion of the Drinfeld moduli schemes in a finite product of infinite Grassmannians, such that they will be locally closed subschemes of these Grassmannians which represent a kind of flag varieties. This construction is derived from two results: the first is that the moduli functor of vector bundles with an ∞-formal level structure (defined below) ove...
متن کاملUniversal moduli spaces of surfaces with flat bundles and cobordism theory
For a compact, connected Lie group G, we study the moduli of pairs (Σ,E), where Σ is a genus g Riemann surface and E →Σ is a flat G-bundle. Varying both the Riemann surface Σ and the flat bundle leads to a moduli space Mg , parametrizing families Riemann surfaces with flat G-bundles. We show that there is a stable range in which the homology of Mg is independent of g. The stable range depends o...
متن کاملFinite rank vector bundles on inductive limits of grassmannians
If P is the projective ind-space, i.e. P is the inductive limit of linear embeddings of complex projective spaces, the Barth-Van de Ven-Tyurin (BVT) Theorem claims that every finite rank vector bundle on P is isomorphic to a direct sum of line bundles. We extend this theorem to general sequences of morphisms between projective spaces by proving that, if there are infinitely many morphisms of de...
متن کاملGrassmannian and string theory
Infinite-dimensional Grassmannian manifold contains moduli spaces of Riemann surfaces of all genera. This well known fact leads to a conjecture that non-perturbative string theory can be formulated in terms of Grassmannian. We present new facts supporting this hypothesis. In particular, it is shown that Grassmannians can be considered as generalized moduli spaces; this statement permits us to d...
متن کامل