In:
Canadian Journal of Mathematics, Canadian Mathematical Society, Vol. 60, No. 1 ( 2008-02-01), p. 33-63
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.
Type of Medium:
Online Resource
ISSN:
0008-414X
,
1496-4279
DOI:
10.4153/CJM-2008-002-7
Language:
English
Publisher:
Canadian Mathematical Society
Publication Date:
2008
detail.hit.zdb_id:
1467410-5
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