A remark on amoebas in higher codimensions

TL;DR

This paper demonstrates that tube sets over amoebas of algebraic varieties and holomorphic chains are q-pseudoconcave, based on their representation as supports of positive closed currents, advancing understanding of their geometric properties.

Contribution

It establishes the q-pseudoconcavity of tube sets over amoebas in higher codimensions using positive closed currents, extending previous results to more general settings.

Findings

Tube sets over amoebas are q-pseudoconcave.

Representation as supports of positive closed currents is key.

Results apply to algebraic varieties and almost periodic holomorphic chains.

Abstract

It is shown that tube sets over amoebas of algebraic varieties (and, more generally, of almost periodic holomorphic chains) of dimension q are q-pseudoconcave in the sense of Rothstein. This is a direct consequence of a representation of such sets as supports of positive closed currents.