Principal bundle, parabolic bundle, and holomorphic connection

Biswas, Indranil

doi:10.1007/978-93-86279-11-8_13

Cited by 4 publications

(7 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A fundamental graded Lie algebra is a nilpotent graded Lie algebra m = p<0 g p generated by g −1 , i.e., g p = [g p+1 , g −1 ] for p < −1. Given a fundamental graded Lie algebra m = p<0 g p , there exists a unique graded Lie algebra g(m) = p∈Z g p (m) such that (1)…”

Section: Prolongations and Cartan Connectionsmentioning

confidence: 99%

“…The tower RP (0) is called universal tower prolonging P (0) . In the proof of Theorem 3.6.1 of [17], we get a tower P (1) and a surjective map P (1) → RP (0) /F 2 where F 2 = F 2 RP (0) . Apply these two theorem again to obtain universal tower RP (1) prolonging P (1) , and a tower P (2) with a surjective map P (2) → RP (1) /F 3 , where F 3 = F 3 RP (1) .…”

Section: The Symbol Algebra Symbmentioning

confidence: 99%

“…In the proof of Theorem 3.6.1 of [17], we get a tower P (1) and a surjective map P (1) → RP (0) /F 2 where F 2 = F 2 RP (0) . Apply these two theorem again to obtain universal tower RP (1) prolonging P (1) , and a tower P (2) with a surjective map P (2) → RP (1) /F 3 , where F 3 = F 3 RP (1) . In this way, starting from P (0) := M × G 0 , we get a tower P which is the limit of the sequence of the bundles (P (0) , P (1) , P (2)…”

Section: The Symbol Algebra Symbmentioning

confidence: 99%

“…Apply these two theorem again to obtain universal tower RP (1) prolonging P (1) , and a tower P (2) with a surjective map P (2) → RP (1) /F 3 , where F 3 = F 3 RP (1) . In this way, starting from P (0) := M × G 0 , we get a tower P which is the limit of the sequence of the bundles (P (0) , P (1) , P (2)…”

Section: The Symbol Algebra Symbmentioning

confidence: 99%

See 3 more Smart Citations

Geometric Structures Modeled on Smooth Projective Horospherical Varieties of Picard Number One

Shin-young

2017

Transformation Groups

View full text Add to dashboard Cite

Geometric structures modeled on rational homogeneous manifolds are studied to characterize rational homogeneous manifolds and to prove their deformation rigidity. To generalize these characterizations and deformation rigidity results to quasihomogeneous varieties, we first study horospherical varieties and geometric structures modeled on horospherical varieties. Using Cartan geometry, we prove that a geometric structure modeled on a smooth projective horospherical variety of Picard number one is locally equivalent to the standard geometric structure when the geometric structure is defined on a Fano manifold of Picard number one.

show abstract

Section: Prolongations and Cartan Connectionsmentioning

confidence: 99%

Section: The Symbol Algebra Symbmentioning

confidence: 99%

Section: The Symbol Algebra Symbmentioning

confidence: 99%

Section: The Symbol Algebra Symbmentioning

confidence: 99%

See 2 more Smart Citations

Geometric Structures Modeled on Smooth Projective Horospherical Varieties of Picard Number One

Shin-young

2017

Transformation Groups

View full text Add to dashboard Cite

show abstract

“…Let D denote the holomorphic connection on the principal G-bundle E G induced by θ (see Section 3). Since M is rationally connected, the curvature of D vanishes (see [4,p. 160,Theorem 3.1]).…”

Section: Cartan Geometries and Rational Curvesmentioning

confidence: 99%

Holomorphic Cartan geometries, Calabi–Yau manifolds and rational curves

Biswas¹,

McKay²

2010

Differential Geometry and its Applications

Self Cite

View full text Add to dashboard Cite

show abstract

Holomorphic Cartan geometry on manifolds with numerically effective tangent bundle

Biswas

Bruzzo²

2011

Differential Geometry and its Applications

View full text Add to dashboard Cite

Let X be a compact connected Kähler manifold such that the holomorphic tangent bundle T X is numerically effective. A theorem of [11] says that there is a finite unramified Galois covering M −→ X, a complex torus T , and a holomorphic surjective submersion f : M −→ T , such that the fibers of f are Fano manifolds with numerically effective tangent bundle. A conjecture of Campana and Peternell says that the fibers of f are rational and homogeneous. Assume that X admits a holomorphic Cartan geometry.We prove that the fibers of f are rational homogeneous varieties. We also prove that the holomorphic principal G-bundle over T given by f , where G is the group of all holomorphic automorphisms of a fiber, admits a flat holomorphic connection.2000 Mathematics Subject Classification. 32M10, 14M17, 53C15.

show abstract

Principal bundle, parabolic bundle, and holomorphic connection

Cited by 4 publications

References 24 publications

Geometric Structures Modeled on Smooth Projective Horospherical Varieties of Picard Number One

Geometric Structures Modeled on Smooth Projective Horospherical Varieties of Picard Number One

Holomorphic Cartan geometries, Calabi–Yau manifolds and rational curves

Holomorphic Cartan geometry on manifolds with numerically effective tangent bundle

Contact Info

Product

Resources

About