Abstract. We classify holomorphic as well as algebraic torus equivariant principal G-bundles over a nonsingular toric variety X, where G is a complex linear algebraic group. It is shown that any such bundle over an affine, nonsingular toric variety admits a trivialization in equivariant sense. We also obtain some splitting results.
Let X be a complete toric variety equipped with the action of a torus T , and G be a reductive algebraic group, defined over C. We introduce the notion of a compatible Σ-filtered algebra associated to X, generalizing the notion of a compatible Σ-filtered vector space due to Klyachko. We combine Klyachko's classification of T -equivariant vector bundles on X with Nori's Tannakian approach to principal G-bundles, to give an equivalence of categories between T -equivariant principal G-bundles on X and certain compatible Σ-filtered algebras associated to X.
Let E G be a Γ-equivariant algebraic principal G-bundle over a normal complex affine variety X equipped with an action of Γ, where G and Γ are complex linear algebraic groups. Suppose X is contractible as a topological Γ-space with a dense orbit, and x 0 ∈ X is a Γ-fixed point. We show that if Γ is reductive, then E G admits a Γ-equivariant isomorphism with the product principal G-bundle X × ρ E G (x 0 ), where ρ : Γ −→ G is a homomorphism between algebraic groups. As a consequence, any torus equivariant principal G-bundle over an affine toric variety is equivariantly trivial. This leads to a classification of torus equivariant principal G-bundles over any complex toric variety, generalizing the main result of [2].
The existence and uniqueness of H-N reduction for the Higgs principal bundles over nonsingular projective variety is shown in this article. We also extend the notion of H-N reduction for (Γ, G)-bundles and ramified G-bundles over a smooth curve.
Abstract. Let PM α s be a moduli space of stable parabolic vector bundles of rank n ≥ 2 and fixed determinant of degree d over a compact connected Riemann surface X of genus g(X) ≥ 2. If g(X) = 2, then we assume that n > 2. Let m denote the greatest common divisor of d, n and the dimensions of all the successive quotients of the quasi-parabolic filtrations. We prove that the Brauer group Br(PM α s ) is isomorphic to the cyclic group Z/mZ. We also show that Br(PM α s ) is generated by the Brauer class of the Brauer-Severi variety over PM α s obtained by restricting the universal projective bundle over X × PM α s .
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