A classification of equivariant principal bundles over nonsingular toric varieties

Biswas, Indranil
Dey, Arijit
Poddar, Mainak
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.


On equivariant Serre problem for principal bundles
Biswas, Indranil; Dey, Arijit; Poddar, Mainak (World Scientific Pub Co Pte Lt, 2018-08-01)
Let E-G be a Gamma-equivariant algebraic principal G-bundle over a normal complex affine variety X equipped with an action of Gamma, where G and Gamma are complex linear algebraic groups. Suppose X is contractible as a topological Gamma-space with a dense orbit, and x(0) is an element of X is a Gamma-fixed point. We show that if Gamma is reductive, then E-G admits a Gamma-equivariant isomorphism with the product principal G-bundle X x rho E-G(x(0)), where rho : Gamma -> G is a homomorphism between algebraic...
On a Fitting length conjecture without the coprimeness condition
Ercan, Gülin (Springer Science and Business Media LLC, 2012-08-01)
Let A be a finite nilpotent group acting fixed point freely by automorphisms on the finite solvable group G. It is conjectured that the Fitting length of G is bounded by the number of primes dividing the order of A, counted with multiplicities. The main result of this paper shows that the conjecture is true in the case where A is cyclic of order p (n) q, for prime numbers p and q coprime to 6 and G has abelian Sylow 2-subgroups.
A formula for the joint local spectral radius
Emel'yanov, EY; Ercan, Z (American Mathematical Society (AMS), 2004-01-01)
We give a formula for the joint local spectral radius of a bounded subset of bounded linear operators on a Banach space X in terms of the dual of X.
A generalisation of a theorem of Koldunov with an elementary proof
Ercan, Z (Institute of Mathematics, Czech Academy of Sciences, 1999-01-01)
We generalize a Theorem of Koldunov [2] and prove that a disjointness preserving quasi-linear operator between Resz spaces has the Hammerstein property.
Relative topology of real algebraic varieties in their complexifications
Ozan, Yıldıray (Mathematical Sciences Publishers, 2004-12-01)
We investigate, for a given smooth closed manifold M, the existence of an algebraic model X for M (i.e., a nonsingular real algebraic variety diffeomorphic to M) such that some nonsingular projective complexification i:X-->X-C of X admits a retraction r:X-C-->X. If such an X exists, we show that M must be formal in the sense of Sullivan's minimal models, and that all rational Massey products on M are trivial.
Citation Formats
I. Biswas, A. Dey, and M. Poddar, “A classification of equivariant principal bundles over nonsingular toric varieties,” INTERNATIONAL JOURNAL OF MATHEMATICS, pp. 0–0, 2016, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/66511.