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Lärkäng, R. och Larusson, F. (2016) *Extending holomorphic maps from Stein manifolds into affine toric varieties*.

** BibTeX **

@article{

Lärkäng2016,

author={Lärkäng, Richard and Larusson, F.},

title={Extending holomorphic maps from Stein manifolds into affine toric varieties},

journal={Proceedings of the American Mathematical Society},

issn={0002-9939},

volume={144},

issue={11},

pages={4613-4626},

abstract={A complex manifold Y is said to have the interpolation property if a holomorphic map to Y from a subvariety S of a reduced Stein space X has a holomorphic extension to X if it has a continuous extension. Taking S to be a contractible submanifold of X = C^n gives an ostensibly much weaker property called the convex interpolation property. By a deep theorem of Forstneric, the two properties are equivalent. They (and about a dozen other nontrivially equivalent properties) define the class of Oka manifolds. This paper is the first attempt to develop Oka theory for singular targets. The targets that we study are affine toric varieties, not necessarily normal. We prove that every affine toric variety satisfies a weakening of the interpolation property that is much stronger than the convex interpolation property, but the full interpolation property fails for most affine toric varieties, even for a source as simple as the product of two annuli embedded in C^4.},

year={2016},

keywords={Stein manifold, Stein space, affine toric variety, holomorphic map, extension, Mathematics },

}

** RefWorks **

RT Journal Article

SR Electronic

ID 243887

A1 Lärkäng, Richard

A1 Larusson, F.

T1 Extending holomorphic maps from Stein manifolds into affine toric varieties

YR 2016

JF Proceedings of the American Mathematical Society

SN 0002-9939

VO 144

IS 11

SP 4613

OP 4626

AB A complex manifold Y is said to have the interpolation property if a holomorphic map to Y from a subvariety S of a reduced Stein space X has a holomorphic extension to X if it has a continuous extension. Taking S to be a contractible submanifold of X = C^n gives an ostensibly much weaker property called the convex interpolation property. By a deep theorem of Forstneric, the two properties are equivalent. They (and about a dozen other nontrivially equivalent properties) define the class of Oka manifolds. This paper is the first attempt to develop Oka theory for singular targets. The targets that we study are affine toric varieties, not necessarily normal. We prove that every affine toric variety satisfies a weakening of the interpolation property that is much stronger than the convex interpolation property, but the full interpolation property fails for most affine toric varieties, even for a source as simple as the product of two annuli embedded in C^4.

LA eng

DO 10.1090/proc/13108

LK http://dx.doi.org/10.1090/proc/13108

OL 30