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1
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Criterion for connections on principal bundles over a pointed Riemann surface

100%
Biswas I.
Complex Manifolds
|
2017
|
tom 4
|
nr 1
155-171
EN
We investigate connections, and more generally logarithmic connections, on holomorphic principal bundles over a compact connected Riemann surface.
2
Content available remote

Holomorphic Cartan geometries and rational curves

64%
Biswas I., McKay B.
Complex Manifolds
|
2016
|
tom 3
|
nr 1
EN
We prove that any compact Kähler manifold bearing a holomorphic Cartan geometry contains a rational curve just when the Cartan geometry is inherited from a holomorphic Cartan geometry on a lower dimensional compact Kähler manifold. This shows that many complex manifolds admit no or few holomorphic Cartan geometries.
3
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Invariant connections and invariant holomorphic bundles on homogeneous manifolds

64%
Biswas I., Teleman A.
Open Mathematics
|
2014
|
tom 12
|
nr 1
1-13
EN
Let X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects: equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when X has an α-invariant complex structure).
4
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Equivariant principal bundles for G–actions and G–connections

51%
Biswas I., Kannan S. S., Nagaraj D. S.
Complex Manifolds
|
2015
|
tom 2
|
nr 1
EN
Given a complex manifold M equipped with an action of a group G, and a holomorphic principal H–bundle EH on M, we introduce the notion of a connection on EH along the action of G, which is called a G–connection. We show some relationship between the condition that EH admits a G–equivariant structure and the condition that EH admits a (flat) G–connection. The cases of bundles on homogeneous spaces and smooth toric varieties are discussed.
5
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The Fujiki class and positive degree maps

51%
Bharali G., Biswas I., Mj M.
Complex Manifolds
|
2015
|
tom 2
|
nr 1
EN
We show that a map between complex-analytic manifolds, at least one ofwhich is in the Fujiki class, is a biholomorphism under a natural condition on the second cohomologies. We use this to establish that, with mild restrictions, a certain relation of “domination” introduced by Gromov is in fact a partial order.
6
Content available remote

The Brauer group of desingularization of moduli spaces of vector bundles over a curve

51%
Biswas I., Hogadi A., Holla Y.
Open Mathematics
|
2012
|
tom 10
|
nr 4
1300-1305
EN
Let C be an irreducible smooth projective curve, of genus at least two, defined over an algebraically closed field of characteristic zero. For a fixed line bundle L on C, let M C (r; L) be the coarse moduli space of semistable vector bundles E over C of rank r with ∧r E = L. We show that the Brauer group of any desingularization of M C(r; L) is trivial.
7
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Unramified Brauer group of the moduli spaces of PGLr(ℂ)-bundles over curves

51%
Biswas I., Hogadi A., Holla Y.
Open Mathematics
|
2014
|
tom 12
|
nr 8
1157-1163
EN
Let X be an irreducible smooth complex projective curve of genus g, with g ≥ 2. Let N be a connected component of the moduli space of semistable principal PGLr (ℂ)-bundles over X; it is a normal unirational complex projective variety. We prove that the Brauer group of a desingularization of N is trivial.
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