Non-degenerate maps and sets

Winkelmann, Jochen

doi:10.1007/s00209-004-0732-2

Cited by 17 publications

(16 citation statements)

References 16 publications

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“…Recall that we do not specify the radius of ∆ in order to lighten the notation. The following is a simple consequence of the ideas developed by Winkelmann in [Win05]. Lemma 6.2.…”

Section: Setup For One-parameter Familiesmentioning

confidence: 89%

The boundary of linear subvarieties

Frederik¹

2020

Preprint

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We describe the boundary of linear subvarieties in the moduli space of multi-scale differentials. Linear subvarieties are algebraic subvarieties of strata of (possibly) meromorphic differentials that in local period coordinates are given by linear equations. The main example of such are affine invariant submanifolds, that is, closures of SL(2, R)-orbits. We prove that the boundary of any linear subvariety is again given by linear equations in generalized period coordinates of the boundary. Our main technical tool is an asymptotic analysis of periods near the boundary of the moduli space of multi-scale differentials which yields further techniques and results of independent interest.

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“…Recall that we do not specify the radius of ∆ in order to lighten the notation. The following is a simple consequence of the ideas developed by Winkelmann in [Win05]. Lemma 6.2.…”

Section: Setup For One-parameter Familiesmentioning

confidence: 89%

The boundary of linear subvarieties

Frederik¹

2020

Preprint

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“…Note that such an f always exists (cf. [12]; according to [2], page 49, this was already known by J. Globevnik).…”

Section: Introduction and Resultsmentioning

confidence: 99%

On the derivatives of the Lempert functions

Nikolov

Pflug

2007

Annali di Matematica

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“…In his paper [10], Winkelmann also proved that any irreducible complex space is D-dominated. Our first main result is the following partial generalization to spaces of holomorphic maps.…”

Section: Introductionmentioning

confidence: 99%

“…O(X, Y ) ∼ = Y . Winkelmann [10] proved that for any irreducible complex space Z admitting a nonconstant bounded holomorphic function, the unit disc D is Z-dominated. Correspondingly, Chen and Wang [3] proved that for any irreducible complex space Z admitting a nonconstant holomorphic function, the complex line C is Z-dominated.…”

Section: Introductionmentioning

confidence: 99%

Dense holomorphic curves in spaces of holomorphic maps and applications to universal maps

Kusakabe

2017

Int. J. Math.

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Abstract. We study when there exists a dense holomorphic curve in a space of holomorphic maps from a Stein space. We first show that for any bounded convex domain Ω ⋐ C n and any connected complex manifold Y , the space O(Ω, Y ) contains a dense holomorphic disc. Our second result states that Y is an Oka manifold if and only if for any Stein space X there exists a dense entire curve in every path component of O(X, Y ).In the second half of this paper, we apply the above results to the theory of universal functions. It is proved that for any bounded convex domain Ω ⋐ C n , any fixed-point-free automorphism of Ω and any connected complex manifold Y , there exists a universal map Ω → Y . We also characterize Oka manifolds by the existence of universal maps.

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Non-degenerate maps and sets

Abstract: Abstract. We construct certain non-degenerate maps and sets, mainly in the complex-analytic category.

Cited by 17 publications

References 16 publications

The boundary of linear subvarieties

The boundary of linear subvarieties

On the derivatives of the Lempert functions

Dense holomorphic curves in spaces of holomorphic maps and applications to universal maps

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