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- W4250355313 abstract "Abstract Let V be an analytic variety in some open set in ℂ n . For a real analytic curve γ with γ(0) = 0 and d ≥ 1, define Vt = t − d ( V − γ( t )). It was shown in a previous paper that the currents of integration over V t converge to a limit current whose support T γ,δ V is an algebraic variety as t tends to zero. Here, it is shown that the canonical defining function of the limit current is the suitably normalized limit of the canonical defining functions of the V t . As a corollary, it is shown that T γ,δ V is either inhomogeneous or coincides with T γ,δ V for all δ in some neighborhood of d . As another application it is shown that for surfaces only a finite number of curves lead to limit varieties that are interesting for the investigation of Phragmén-Lindelöf conditions. Corresponding results for limit varieties T σ,δ W of algebraic varieties W along real analytic curves tending to infinity are derived by a reduction to the local case." @default.
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- W4250355313 date "2008-02-01" @default.
- W4250355313 modified "2023-10-17" @default.
- W4250355313 title "Higher Order Tangents to Analytic Varieties along Curves. II" @default.
- W4250355313 doi "https://doi.org/10.4153/cjm-2008-002-7" @default.
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