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Determinant bundle over the universal moduli space of vector bundles over the Teichmüller space

Indranil Biswas — 1997

Annales de l'institut Fourier

The moduli space of stable vector bundles over a moving curve is constructed, and on this a generalized Weil-Petersson form is constructed. Using the local Riemann-Roch formula of Bismut-Gillet-Soulé it is shown that the generalized Weil-Petersson form is the curvature of the determinant line bundle, equipped with the Quillen metric, for a vector bundle on the fiber product of the universal moduli space with the universal curve.

On the Hodge cycles of Prym varieties

Indranil Biswas — 2004

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We show that the Néron–Severi group of the Prym variety for a degree three unramified Galois covering of a hyperelliptic Riemann surface has a distinguished subgroup of rank three. For the general hyperelliptic curve, the algebra of Hodge cycles on the Prym variety is generated by this group of rank three.

Orbifold principal bundles on an elliptic fibration and parabolic principal bundles on a Riemann surface.

Indranil Biswas — 2003

Collectanea Mathematica

Let X be a compact Riemann surface and associated to each point p-i of a finite subset S of X is a positive integer m-i. Fix an elliptic curve C. To this data we associate a smooth elliptic surface Z fibered over X. The group C acts on Z with X as the quotient. It is shown that the space of all vector bundles over Z equipped with a lift of the action of C is in bijective correspondence with the space of all parabolic bundles over X with parabolic structure over S and the parabolic weights at any...

Invariant connections and invariant holomorphic bundles on homogeneous manifolds

Indranil BiswasAndrei Teleman — 2014

Open Mathematics

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...

Holomorphic Cartan geometries and rational curves

Indranil BiswasBenjamin McKay — 2016

Complex Manifolds

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.

Higgs bundles and representation spaces associated to morphisms

Indranil BiswasCarlos Florentino — 2015

Archivum Mathematicum

Let G be a connected reductive affine algebraic group defined over the complex numbers, and K G be a maximal compact subgroup. Let X , Y be irreducible smooth complex projective varieties and f : X Y an algebraic morphism, such that π 1 ( Y ) is virtually nilpotent and the homomorphism f * : π 1 ( X ) π 1 ( Y ) is surjective. Define f ( π 1 ( X ) , G ) = { ρ Hom ( π 1 ( X ) , G ) A ρ factors through f * } , f ( π 1 ( X ) , K ) = { ρ Hom ( π 1 ( X ) , K ) A ρ factors through f * } , where A : G GL ( Lie ( G ) ) is the adjoint action. We prove that the geometric invariant theoretic quotient f ( π 1 ( X , x 0 ) , G ) / / G admits a deformation retraction to f ( π 1 ( X , x 0 ) , K ) / K . We also show that the space of conjugacy classes of n almost commuting elements...

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

Indranil BiswasAmit HogadiYogish Holla — 2012

Open Mathematics

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.

The Fujiki class and positive degree maps

Gautam BharaliIndranil BiswasMahan Mj — 2015

Complex Manifolds

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.

A criterion for virtual global generation

Indranil BiswasA. J. Parameswaran — 2006

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let X be a smooth projective curve defined over an algebraically closed field k , and let F X denote the absolute Frobenius morphism of X when the characteristic of k is positive. A vector bundle over X is called virtually globally generated if its pull back, by some finite morphism to X from some smooth projective curve, is generated by its global sections. We prove the following. If the characteristic of k is positive, a vector bundle E over X is virtually globally generated if and only if ( F X m ) * E E a E f for...

Equivariant principal bundles for G–actions and G–connections

Indranil BiswasS. Senthamarai KannanD. S. Nagaraj — 2015

Complex Manifolds

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.

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