Eight lectures on Oka manifolds

Larusson, Finnur

doi:10.48550/arxiv.1405.7212

2014

DOI: 10.48550/arxiv.1405.7212

|View full text |Cite

Preprint

Eight lectures on Oka manifolds

Finnur Larusson

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2017

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 23 publications

(45 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For basic introductions to Oka theory, see [25] and [26]. For more comprehensive references, see [10], [11] and [12].…”

mentioning

confidence: 99%

Holomorphic Flexibility Properties of Spaces of Elliptic Functions

Bowman

2017

Bull. Aust. Math. Soc.

View full text Add to dashboard Cite

Let X be an elliptic curve and P the Riemann sphere. Since X is compact, it is a deep theorem of Douady that the set O(X, P) consisting of holomorphic maps X → P admits a complex structure. If R n denotes the set of maps of degree n, then Namba has shown for n ≥ 2 that R n is a 2n-dimensional complex manifold. We study holomorphic flexibility properties of the spaces R 2 and R 3 .Firstly, we show that R 2 is homogeneous and hence an Oka manifold. Secondly, we present our main theorem, that there is a six-sheeted branched covering space of R 3 that is an Oka manifold. It follows that R 3 is C-connected and dominable. We show that R 3 is Oka if and only if P 2 \C is Oka, where C is a cubic curve that is the image of a certain embedding of X into P 2 .We investigate the strong dominability of R 3 and show that if X is not biholomorphic to C/Γ 0 , where Γ 0 is the hexagonal lattice, then R 3 is strongly dominable.As a Lie group, X acts freely on R 3 by precomposition by translations. We show that R 3 is holomorphically convex and that the quotient space R 3 /X is a Stein manifold.We construct an alternative six-sheeted Oka branched covering space of R 3 and prove that it is isomorphic to our first construction in a natural way. This alternative construction gives us an easier way of interpreting the fibres of the branched covering map.The full thesis is available at https://arxiv.org/abs/1609.07184.

show abstract

“…For basic introductions to Oka theory, see [25] and [26]. For more comprehensive references, see [10], [11] and [12].…”

mentioning

confidence: 99%

Holomorphic Flexibility Properties of Spaces of Elliptic Functions

Bowman

2017

Bull. Aust. Math. Soc.

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Eight lectures on Oka manifolds

Cited by 1 publication

References 23 publications

Holomorphic Flexibility Properties of Spaces of Elliptic Functions

Holomorphic Flexibility Properties of Spaces of Elliptic Functions

Contact Info

Product

Resources

About