Holomorphic Cartan geometries and rational curves

Indranil Biswas; Benjamin McKay

doi:10.1515/coma-2016-0004

Holomorphic Cartan geometries and rational curves

Indranil Biswas
, Benjamin McKay

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	145-168
Number of pages	24
Journal	Complex Manifolds
Volume	3
Issue number	1
DOIs	https://doi.org/10.1515/coma-2016-0004
Publication status	Published - Jan 2016
Externally published	Yes

Access to Document

10.1515/coma-2016-0004

Cite this

@article{b83725ae5167474ea07f28635ef758c5,

title = "Holomorphic Cartan geometries and rational curves",

abstract = "We prove that any compact K{\"a}hler 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 K{\"a}hler manifold. This shows that many complex manifolds admit no or few holomorphic Cartan geometries.",

author = "Indranil Biswas and Benjamin McKay",

note = "Publisher Copyright: {\textcopyright} 2016 K. Leschke and K. Moriya, published by De Gruyter Open.",

year = "2016",

month = jan,

doi = "10.1515/coma-2016-0004",

language = "English",

volume = "3",

pages = "145--168",

journal = "Complex Manifolds",

issn = "2300-7443",

publisher = "Walter de Gruyter GmbH",

number = "1",

}

TY - JOUR

T1 - Holomorphic Cartan geometries and rational curves

AU - Biswas, Indranil

AU - McKay, Benjamin

PY - 2016/1

Y1 - 2016/1

N2 - 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.

AB - 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.

UR - https://www.scopus.com/pages/publications/84994900275

U2 - 10.1515/coma-2016-0004

DO - 10.1515/coma-2016-0004

M3 - Article

AN - SCOPUS:84994900275

SN - 2300-7443

VL - 3

SP - 145

EP - 168

JO - Complex Manifolds

JF - Complex Manifolds

IS - 1

ER -

Holomorphic Cartan geometries and rational curves

Abstract

Access to Document

Other files and links

Fingerprint

Cite this