A Remark on δ-cohomology with supports in the complement of a cone singularity

Adam Harris

A Remark on δ-cohomology with supports in the complement of a cone singularity

Adam Harris

Mathematics

Research output: Contribution to conference › Paper › peer-review

Abstract

Let [this equation] be a ∂-closed form on ℂⁿ x ℂ. If it is assumed that ψ has compact (specifically non-empty) support, then ψn+1(w,z) ≠ 0, for if the last component vanishes identically then this, together with the closedness of ψ, implies that [this second equation] vanishes identically, 1 ≤ k ≤ n. Hence ψ is the pullback of a form defined on ℂⁿ, which contradicts the compactness of support.

Original language	English
Pages	32-37
Publication status	Published - Aug 2007
Event	JARCS 2007: Second Japanese-Australian Workshop on Real and Complex Singularities - Kyoto, Japan Duration: 26 Nov 2007 → 29 Nov 2007

Conference

Conference	JARCS 2007: Second Japanese-Australian Workshop on Real and Complex Singularities
City	Kyoto, Japan
Period	26/11/07 → 29/11/07

Keywords

Real and Complex Functions (incl Several Variables)

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https://hdl.handle.net/1959.11/4626

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title = "A Remark on δ-cohomology with supports in the complement of a cone singularity",

abstract = "Let [this equation] be a ∂-closed form on ℂⁿ x ℂ. If it is assumed that ψ has compact (specifically non-empty) support, then ψn+1(w,z) ≠ 0, for if the last component vanishes identically then this, together with the closedness of ψ, implies that [this second equation] vanishes identically, 1 ≤ k ≤ n. Hence ψ is the pullback of a form defined on ℂⁿ, which contradicts the compactness of support.",

keywords = "Real and Complex Functions (incl Several Variables)",

author = "Adam Harris",

year = "2007",

month = aug,

language = "English",

pages = "32--37",

note = "JARCS 2007: Second Japanese-Australian Workshop on Real and Complex Singularities ; Conference date: 26-11-2007 Through 29-11-2007",

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AU - Harris, Adam

PY - 2007/8

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N2 - Let [this equation] be a ∂-closed form on ℂⁿ x ℂ. If it is assumed that ψ has compact (specifically non-empty) support, then ψn+1(w,z) ≠ 0, for if the last component vanishes identically then this, together with the closedness of ψ, implies that [this second equation] vanishes identically, 1 ≤ k ≤ n. Hence ψ is the pullback of a form defined on ℂⁿ, which contradicts the compactness of support.

AB - Let [this equation] be a ∂-closed form on ℂⁿ x ℂ. If it is assumed that ψ has compact (specifically non-empty) support, then ψn+1(w,z) ≠ 0, for if the last component vanishes identically then this, together with the closedness of ψ, implies that [this second equation] vanishes identically, 1 ≤ k ≤ n. Hence ψ is the pullback of a form defined on ℂⁿ, which contradicts the compactness of support.

KW - Real and Complex Functions (incl Several Variables)

UR - http://www.rimath.saitama-u.ac.jp/lab.jp/Fukui/2007/JARCS2.html

M3 - Paper

SP - 32

EP - 37

T2 - JARCS 2007: Second Japanese-Australian Workshop on Real and Complex Singularities

Y2 - 26 November 2007 through 29 November 2007

ER -

A Remark on δ-cohomology with supports in the complement of a cone singularity

Abstract

Conference

Keywords

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