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no. 4
$T$-Polynomial Convexity and Holomorphic Convexity
Blake J. Boudreaux1
1 Department of Mathematics, Middlesex College, The University of Western Ontario, London, Ontario, Canada, N6A 5B7
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 34 (2025) no. 4, pp. 1147-1157

We compare the $T$-polynomial convexity of Guedj with holomorphic convexity away from the support of $T$. In particular, we prove an Oka–Weil theorem for $T$-polynomial convexity. We also show a sufficient condition for when the notions of $T$-polynomial convexity and holomorphic convexity of $X\setminus \mathop {\mathrm{Supp}} T$ coincide in the class of complex projective algebraic manifolds.

Nous comparons la convexité $T$-polynomiale de Guedj avec la convexité holomorphe sur le complément du support de $T$. En particulier, nous démontrons un théorème d’Oka–Weil pour la convexité $T$-polynomiale. Nous montrons également une condition suffisante pour que les notions de convexité $T$-polynomiale et de convexité holomorphe de $X\setminus \mathop {\mathrm{Supp}}T$ coïncident dans la classe des variétés algébriques projectives complexes.

Received:
Accepted:
Published online:
DOI: 10.5802/afst.1828
Classification: 32E05, 32U40
Keywords: holomorphic convexity, polynomial convexity, Stein manifolds, complex projective manifolds
Mots-clés : semblable banalité, autosimilarité logarithmique, loi de Gauß

Blake J. Boudreaux 1

1 Department of Mathematics, Middlesex College, The University of Western Ontario, London, Ontario, Canada, N6A 5B7
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Blake J. Boudreaux. $T$-Polynomial Convexity and Holomorphic Convexity. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 34 (2025) no. 4, pp. 1147-1157. doi: 10.5802/afst.1828

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