Principal bundles over projective manifolds with parabolic structure over a divisor

Balaji, V.; Biswas, Indranil; Nagaraj, D. S.

doi:10.2748/tmj/1178207416

Cited by 62 publications

(96 citation statements)

References 30 publications

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“…It is straightforward to check that PVect(X, D, N ) is closed under all the above operations, namely parabolic tensor product, direct sum and taking the parabolic dual. The proof is given in [1].…”

Section: The Parabolic Analog Of Principal Bundlesmentioning

confidence: 99%

“…In [1] we construct a map from [Γ, G, N] to P G(X, D, N ) and also a map from P G(X, D, N ) to [Γ, G, N]. Using the result of Nori, the constructions reduce to a construction of maps between parabolic vector bundles and orbifold vector bundles.…”

Section: Orbifold Bundles and Parabolic Bundlesmentioning

confidence: 99%

“…The following theorem is proved in [1]. The definition of Chern classes of parabolic bundles is given in [5].…”

Section: Proposition 35 If G −→ H Is a Homomorphism Of Groups And Imentioning

confidence: 99%

“…This indicates how we may define semistability in the context of parabolic G-bundles. The following proposition, which is proved in [1], will be needed for that purpose. The definition of parabolic semistable and parabolic polystable vector bundles is given in [9] and [8].…”

Section: Definition 31 ([12]mentioning

confidence: 99%

“…We are very grateful to M. S. Narasimhan for his comments on [1] which led us to the parabolic G-objects defined in Section 5.…”

mentioning

confidence: 99%

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Principal bundles with parabolic structure

Balaji

Biswas

Nagaraj

2001

Electron. Res. Announc. Amer. Math. Soc.

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Section: The Parabolic Analog Of Principal Bundlesmentioning

confidence: 99%

Section: Orbifold Bundles and Parabolic Bundlesmentioning

confidence: 99%

“…The following theorem is proved in [1]. The definition of Chern classes of parabolic bundles is given in [5].…”

Section: Proposition 35 If G −→ H Is a Homomorphism Of Groups And Imentioning

confidence: 99%

Section: Definition 31 ([12]mentioning

confidence: 99%

“…We are very grateful to M. S. Narasimhan for his comments on [1] which led us to the parabolic G-objects defined in Section 5.…”

mentioning

confidence: 99%

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Principal bundles with parabolic structure

Balaji

Biswas

Nagaraj

2001

Electron. Res. Announc. Amer. Math. Soc.

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The Construction Problem in Kähler Geometry

Simpson

2004

International Mathematical Series

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One of the most surprising things in algebraic geometry is the fact that algebraic varieties over the complex numbers benefit from a collection of metric properties which strongly influence their topological and geometric shapes. The existence of a Kähler metric leads to all sorts of Hodge theoretical restrictions on the homotopy types of algebraic varieties. On the other hand, a sparse collection of examples shows that the remaining liberty is nontrivially large. Paradoxically, with all of this information, the research field remains as wide open as it was many decades ago, because the gap between the known restrictions, and the known examples of what can occur, only seems to grow wider and wider the more closely we look at it.In spite of the differential-geometric nature of the questions and methods, the origins of the situation are very algebraic. We look at subvarieties of projective space over the complex numbers. The main over-arching problem in algebraic geometry is to understand the classification of algebro-geometric objects. The topology of the usual complex-valued points of a variety plays an important role, because the topological type is a locally constant function on any classifying space. Thus the partitioning of the classification problem according to topological type provides a coarse, and more calculable, alternative to the partition by connected components. Furthermore, the topology of a variety strongly influences its geometric properties. A sociological observation is that the quest for understanding the topology of algebraic varieties has led to a rich set of techniques which found applications elsewhere, even in physics.Perhaps a word about the choice of ground field is appropriate. One could also look at the shapes of the real points of real algebraic varieties. However, by Weierstrass approximation, pretty much anything can arise if you let the degree get big enough. Thus the classical question in this case is "which shapes can occur for a given degree?" This is so much more difficult 1

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Principal bundle, parabolic bundle, and holomorphic connection

Biswas

2003

A Tribute to C. S. Seshadri

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Principal bundles over projective manifolds with parabolic structure over a divisor

Cited by 62 publications

References 30 publications

Principal bundles with parabolic structure

Principal bundles with parabolic structure

The Construction Problem in Kähler Geometry

Principal bundle, parabolic bundle, and holomorphic connection

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