Bounded meromorphic functions on the complex 2-disc

János Kollár

doi:10.1007/s10998-023-00538-1

Bounded meromorphic functions on the complex 2-disc

János Kollár

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We describe bounded, holomorphic functions on the complex 2-disc that admit a meromorphic extension to a larger 2-disc. This solves a conjecture of Bickel, Knese, Pascoe and Sola. The key technical ingredient is an old theorem of Zariski about integrally closed ideals in 2-dimensional regular rings.

Original language	English (US)
Journal	Periodica Mathematica Hungarica
DOIs	https://doi.org/10.1007/s10998-023-00538-1
State	Accepted/In press - 2023

All Science Journal Classification (ASJC) codes

Mathematics(all)

Keywords

Integral closure
Meromorphic function
Polydisc

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10.1007/s10998-023-00538-1

Cite this

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title = "Bounded meromorphic functions on the complex 2-disc",

abstract = "We describe bounded, holomorphic functions on the complex 2-disc that admit a meromorphic extension to a larger 2-disc. This solves a conjecture of Bickel, Knese, Pascoe and Sola. The key technical ingredient is an old theorem of Zariski about integrally closed ideals in 2-dimensional regular rings.",

keywords = "Integral closure, Meromorphic function, Polydisc",

author = "J{\'a}nos Koll{\'a}r",

note = "Funding Information: I thank K. Bickel, G. Knese, J. E. Pascoe and A. Sola for the conjecture and e-mail discussions; L. Lempert and I. Swanson for helpful suggestions and references. Partial financial support was provided by the NSF under grant number DMS-1901855. Publisher Copyright: {\textcopyright} 2023, Akad{\'e}miai Kiad{\'o}, Budapest, Hungary.",

year = "2023",

doi = "10.1007/s10998-023-00538-1",

language = "English (US)",

journal = "Periodica Mathematica Hungarica",

issn = "0031-5303",

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T1 - Bounded meromorphic functions on the complex 2-disc

AU - Kollár, János

N1 - Funding Information: I thank K. Bickel, G. Knese, J. E. Pascoe and A. Sola for the conjecture and e-mail discussions; L. Lempert and I. Swanson for helpful suggestions and references. Partial financial support was provided by the NSF under grant number DMS-1901855. Publisher Copyright: © 2023, Akadémiai Kiadó, Budapest, Hungary.

PY - 2023

Y1 - 2023

N2 - We describe bounded, holomorphic functions on the complex 2-disc that admit a meromorphic extension to a larger 2-disc. This solves a conjecture of Bickel, Knese, Pascoe and Sola. The key technical ingredient is an old theorem of Zariski about integrally closed ideals in 2-dimensional regular rings.

AB - We describe bounded, holomorphic functions on the complex 2-disc that admit a meromorphic extension to a larger 2-disc. This solves a conjecture of Bickel, Knese, Pascoe and Sola. The key technical ingredient is an old theorem of Zariski about integrally closed ideals in 2-dimensional regular rings.

KW - Integral closure

KW - Meromorphic function

KW - Polydisc

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U2 - 10.1007/s10998-023-00538-1

DO - 10.1007/s10998-023-00538-1

M3 - Article

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SN - 0031-5303

JO - Periodica Mathematica Hungarica

JF - Periodica Mathematica Hungarica

ER -

Bounded meromorphic functions on the complex 2-disc

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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