Higher order approximations at infinity to algebraic varieties

Abstract

Let V be an algebraic variety in Cⁿ. For a curve γ in Cⁿ, going out to infinity, and d ≤ 1, define V_t := t^d(V γ(t)). Then the currents defined by V_t 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.