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Holomorphic convexity of pseudoconvex spaces in terms of the rank of structural sheaf

  • Viorel Vîjîitu EMAIL logo
Published/Copyright: March 1, 2022
Forum Mathematicum
From the journal Forum Mathematicum Volume 34 Issue 2

Abstract

We prove that a pseudoconvex complex space X of pure dimension n+1 is holomorphically convex provided that its singular set has only compact connected components (e.g., X has isolated singularities) and rankx⁡𝒪X=n for all smooth points x outside a compact set of X. This extends a known result due to Ohsawa asserting that a weakly 1-complete, smooth complex surface is holomorphically convex if it admits a globally defined non-constant holomorphic function. We also revise an example of Markoe concerning non-invariance of holomorphic convexity under normalization.

Keywords: Holomorphic convexity; pseudoconvex space; Riemann domain; Hausdorff measure; weakly normal space
MSC 2010: 32E05; 32E10; 32E40; 32F10; 32T99

Communicated by Shigeharu Takayama

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Received: 2021-10-10
Revised: 2021-12-11
Published Online: 2022-03-01
Published in Print: 2022-03-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. On the variance of the nodal volume of arithmetic random waves
  3. On length densities
  4. On weighted compactness of commutators of bilinear maximal Calderón–Zygmund singular integral operators
  5. Geometric nilpotent Lie algebras and zero-dimensional simple complete intersection singularities
  6. On cutting blocking sets and their codes
  7. Inertia groups and smooth structures on quaternionic projective spaces
  8. On the number of zeros of diagonal quartic forms over finite fields
  9. Weak martingale Hardy-type spaces associated with quasi-Banach function lattice
  10. A dual version of Huppert's ρ-σ conjecture for character codegrees
  11. A topological correspondence between partial actions of groups and inverse semigroup actions
  12. On homotopy braids
  13. Holomorphic convexity of pseudoconvex spaces in terms of the rank of structural sheaf
  14. The Shintani double zeta functions
  15. Homological dimensions relative to preresolving subcategories II
  16. Simplicity of indecomposable set-theoretic solutions of the Yang–Baxter equation
  17. A converse theorem for quasimodular forms
https://doi.org/10.1515/forum-2021-0262
Keywords for this article
Holomorphic convexity; pseudoconvex space; Riemann domain; Hausdorff measure; weakly normal space

Articles in the same Issue

  1. Frontmatter
  2. On the variance of the nodal volume of arithmetic random waves
  3. On length densities
  4. On weighted compactness of commutators of bilinear maximal Calderón–Zygmund singular integral operators
  5. Geometric nilpotent Lie algebras and zero-dimensional simple complete intersection singularities
  6. On cutting blocking sets and their codes
  7. Inertia groups and smooth structures on quaternionic projective spaces
  8. On the number of zeros of diagonal quartic forms over finite fields
  9. Weak martingale Hardy-type spaces associated with quasi-Banach function lattice
  10. A dual version of Huppert's ρ-σ conjecture for character codegrees
  11. A topological correspondence between partial actions of groups and inverse semigroup actions
  12. On homotopy braids
  13. Holomorphic convexity of pseudoconvex spaces in terms of the rank of structural sheaf
  14. The Shintani double zeta functions
  15. Homological dimensions relative to preresolving subcategories II
  16. Simplicity of indecomposable set-theoretic solutions of the Yang–Baxter equation
  17. A converse theorem for quasimodular forms
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