A compactification of (ℂ*)4 with no non-constant meromorphic functions

Jun Muk Hwang; Dror Varolin

doi:10.5802/aif.1884

A compactification of (ℂ*)⁴ with no non-constant meromorphic functions

Jun Muk Hwang
, Dror Varolin

Mathematics

Stony Brook University

Korea Institute for Advanced Study

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

2 Scopus citations

Abstract

For each 2-dimensional complex torus T, we construct a compact complex manifold X(T) with a ℂ²-action, which compactifies (ℂ*)⁴ such that the quotient of (ℂ*)⁴ by the ℂ²-action is biholomorphic to T. For a general T, we show that X(T) has no non-constant meromorphic functions.

Original language	English
Pages (from-to)	245-253+VII+XI
Journal	Annales de l'Institut Fourier
Volume	52
Issue number	1
DOIs	https://doi.org/10.5802/aif.1884
State	Published - 2002

Keywords

Compactification
Complex torus

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abstract = "For each 2-dimensional complex torus T, we construct a compact complex manifold X(T) with a ℂ2-action, which compactifies (ℂ*)4 such that the quotient of (ℂ*)4 by the ℂ2-action is biholomorphic to T. For a general T, we show that X(T) has no non-constant meromorphic functions.",

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AU - Hwang, Jun Muk

AU - Varolin, Dror

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AB - For each 2-dimensional complex torus T, we construct a compact complex manifold X(T) with a ℂ2-action, which compactifies (ℂ*)4 such that the quotient of (ℂ*)4 by the ℂ2-action is biholomorphic to T. For a general T, we show that X(T) has no non-constant meromorphic functions.

KW - Compactification

KW - Complex torus

UR - https://www.scopus.com/pages/publications/0038506022

U2 - 10.5802/aif.1884

DO - 10.5802/aif.1884

M3 - Article

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SP - 245-253+VII+XI

JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 1

ER -

A compactification of (ℂ*)⁴ with no non-constant meromorphic functions

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Keywords

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