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$T$-polynomial convexity and holomorphic convexity

Blake J. Boudreaux

Abstract

We compare the $T$-polynomial convexity of Guedj with holomorphic convexity away from the support of $T$. In particular we show an Oka--Weil theorem for $T$-polynomial convexity, as well as present a situation when the notions of $T$-polynomial convexity and holomorphic convexity of $X\setminus\text{Supp }T$ coincide in the context of complex projective algebraic manifolds.

$T$-polynomial convexity and holomorphic convexity

Abstract

We compare the -polynomial convexity of Guedj with holomorphic convexity away from the support of . In particular we show an Oka--Weil theorem for -polynomial convexity, as well as present a situation when the notions of -polynomial convexity and holomorphic convexity of coincide in the context of complex projective algebraic manifolds.
Paper Structure (3 sections, 6 theorems, 22 equations)

This paper contains 3 sections, 6 theorems, 22 equations.

Table of Contents

  1. Introduction and Preliminaries
  2. $T$-polynomial convexity and holomorphic convexity of $X\setminus\text{Supp }T$
  3. Proof of Theorem \ref{['Guedjthm']}

Key Result

Theorem 2

Let $T$ be a positive closed current of bidegree $(1,1)$ satisfying condition (C) on a projective algebraic manifold $X$. Assume $[T]=c_1(L)$ for some positive holomorphic line bundle $L$ on $X$. Suppose that the compact set $K\subset X\setminus\text{Supp }T$ is $T$-polynomially convex and that $f\i

Theorems & Definitions (13)

  • Definition 1
  • Theorem 2
  • Remark
  • Theorem 3
  • Theorem 4: CoGuZe2013
  • Corollary 5
  • proof
  • Theorem 6: c.f. Gu99
  • proof : Proof of Theorem \ref{['OkaWeil']}
  • proof : Proof of Theorem \ref{['HoloTPoly']}
  • ...and 3 more