Cone structures and parabolic geometries

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F22%3A00125176" target="_blank" >RIV/00216224:14310/22:00125176 - isvavai.cz</a>

Result on the web

<a href="https://link.springer.com/article/10.1007%2Fs00208-021-02208-4" target="_blank" >https://link.springer.com/article/10.1007%2Fs00208-021-02208-4</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00208-021-02208-4" target="_blank" >10.1007/s00208-021-02208-4</a>

Result language

angličtina

Original language name

Cone structures and parabolic geometries

Original language description

A cone structure on a complex manifold M is a closed submanifold C⊂PTM of the projectivized tangent bundle which is submersive over M. A conic connection on C specifies a distinguished family of curves on M in the directions specified by C. There are two common sources of cone structures and conic connections, one in differential geometry and another in algebraic geometry. In differential geometry, we have cone structures induced by the geometric structures underlying holomorphic parabolic geometries, a classical example of which is the null cone bundle of a holomorphic conformal structure. In algebraic geometry, we have the cone structures consisting of varieties of minimal rational tangents (VMRT) given by minimal rational curves on uniruled projective manifolds. The local invariants of the cone structures in parabolic geometries are given by the curvature of the parabolic geometries, the nature of which depend on the type of the parabolic geometry, i.e., the type of the fibers of C→M. For the VMRT-structures, more intrinsic invariants of the conic connections which do not depend on the type of the fiber play important roles. We study the relation between these two different aspects for the cone structures induced by parabolic geometries associated with a long simple root of a complex simple Lie algebra. As an application, we obtain a local differential-geometric version of the global algebraic-geometric recognition theorem due to Mok and Hong–Hwang. In our local version, the role of rational curves is completely replaced by appropriate torsion conditions on the conic connection.

Czech name

—

Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

10101 - Pure mathematics

Project

<a href="/en/project/GX19-28628X" target="_blank" >GX19-28628X: Homotopy and Homology Methods and Tools Related to Mathematical Physics</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2022

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematische Annalen

ISSN

0025-5831

e-ISSN

1432-1807

Volume of the periodical

383

Issue of the periodical within the volume

1-2

Country of publishing house

DE - GERMANY

Number of pages

45

Pages from-to

715-759

UT code for WoS article

000659801200001

EID of the result in the Scopus database

2-s2.0-85107502551