A residue criterion for strong holomorphicity
Mats Andersson
TL;DR
This paper introduces a residue-based local criterion to determine strong holomorphicity of meromorphic functions on complex analytic varieties, extending previous results to more general cases.
Contribution
It generalizes Tsikh's residue criterion from reduced complete intersections to arbitrary pure-dimensional analytic varieties.
Findings
Provides a residue current criterion for strong holomorphicity.
Extends previous results to broader classes of varieties.
Offers a new tool for analyzing meromorphic functions on complex varieties.
Abstract
We give a local criterion in terms of a residue current for strong holomorphicity of a meromorphic function on an arbitrary pure-dimensional analytic variety. This generalizes a result by A Tsikh for the case of a reduced complete intersection.
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Taxonomy
TopicsMeromorphic and Entire Functions · Algebraic Geometry and Number Theory · Polynomial and algebraic computation