Higher order approximations at infinity to algebraic varieties


Let V be an algebraic variety in Cn. For a curve γ in Cn, going out to infinity, and d ≤ 1, define Vt := td(V γ(t)). Then the currents defined by Vt converge to a limit current as t tends to infinity. This limit current is either zero or its support is an algebraic variety. Properties of such limit current and examples are presented. These results are useful in the study of solvability questions for partial differential operators via Phragmén-Lindelöf conditions.

DOI Code: 10.1285/i15900932v25n1p103

Keywords: Phragmén-Lindelöf condition; Approximation of algebraic varieties; Holomorphic chain

Classification: 32C25

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