Duke Mathematical Journal

Holomorphic curves in complex spaces

Barbara Drinovec Drnovšek and Franc Forstnerič

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Abstract

We study the existence of topologically closed complex curves normalized by bordered Riemann surfaces in complex spaces. Our main result is that such curves abound in any noncompact complex space admitting an exhaustion function whose Levi form has at least two positive eigenvalues at every point outside a compact set, and this condition is essential. We also construct a Stein neighborhood basis of any compact complex curve with $\mathcal{C}^2$-boundary in a complex space

Article information

Source
Duke Math. J. Volume 139, Number 2 (2007), 203-253.

Dates
First available in Project Euclid: 31 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1185891823

Digital Object Identifier
doi:10.1215/S0012-7094-07-13921-8

Mathematical Reviews number (MathSciNet)
MR2352132

Zentralblatt MATH identifier
1133.32002

Subjects
Primary: 32C25: Analytic subsets and submanifolds 32F32: Analytical consequences of geometric convexity (vanishing theorems, etc.) 32H02: Holomorphic mappings, (holomorphic) embeddings and related questions 32H35: Proper mappings, finiteness theorems
Secondary: 14H55: Riemann surfaces; Weierstrass points; gap sequences [See also 30Fxx]

Citation

Drinovec Drnovšek, Barbara; Forstnerič, Franc. Holomorphic curves in complex spaces. Duke Math. J. 139 (2007), no. 2, 203--253. doi:10.1215/S0012-7094-07-13921-8. https://projecteuclid.org/euclid.dmj/1185891823.


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