Generalized holomorphic Cartan geometries View Full Text


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Article Info

DATE

2019-03-12

AUTHORS

Indranil Biswas, Sorin Dumitrescu

ABSTRACT

This is largely a survey paper, dealing with Cartan geometries in the complex analytic category. We first remind some standard facts going back to the seminal works of Felix Klein, Élie Cartan and Charles Ehresmann. Then we present the concept of a branched holomorphic Cartan geometry which was introduced by Biswas and Dumitrescu (Int Math Res Not IMRN, 2017. 10.1093/imrn/rny003, arxiv:1706.04407). It generalizes to higher dimension the notion of a branched (flat) complex projective structure on a Riemann surface introduced by Mandelbaum. This new framework is much more flexible than that of the usual holomorphic Cartan geometries (e.g. all compact complex projective manifolds admit branched holomorphic projective structures). At the same time, this new definition is rigid enough to enable us to classify branched holomorphic Cartan geometries on compact simply connected Calabi–Yau manifolds. More... »

PAGES

1-20

References to SciGraph publications

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/s40879-019-00327-6

DOI

http://dx.doi.org/10.1007/s40879-019-00327-6

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https://app.dimensions.ai/details/publication/pub.1112703673


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