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Zbl 0877.53013
Hénaut, Alain
Characterization of webs of $\bbfC\sp 2$ whose rank is maximal and which are linearizable. (Caractérisation des tissus de $\bbfC\sp 2$ dont le rang est maximale et qui sont linéarisables.) (French)
[J] Compos. Math. 94, No.3, 247-268 (1994). ISSN 0010-437X; ISSN 1570-5846/e

This paper considers the question of {\it S.-S. Chern} [Bull. Am. Math. Soc., New Ser. 6, 1-8 (1982; Zbl 0483.53013)] on the determination of the $d$-webs of $\bbfC^2$ whose rank is maximum and which are linearisable. The main result is a characterization of these webs for $d\ge 4$ by means of the notion of the ``polynôme associé'' of a $d$-web introduced in [{\it A. Hénaut}, Topology 32, 531-542 (1993; Zbl 0799.32010)] as well as by the geometric properties of the space of Abel's relations of a web [{\it S. S. Chern} and {\it P. Griffiths}, Jahresber. DMV 80, 13-110 (1978; Zbl 0386.14002)]. All the possible linearizations of the above webs are also described, and special cases that had been studied in the third chapter of the book of {\it W. Blaschke} and {\it G. Bol} [Geometrie der Gewebe (Grundlehren 49, Springer, Berlin) (1938; Zbl 0020.06701)] are extended.\par The appendix of this paper contains some classical theorems on algebraic curves in $P^2$ and their proofs, focusing on the geometry of linear webs of $\bbfC^2$.
[D.Papadopoulou-Florou (Thessaloniki)]

MSC 2000:: *53A60 Geometry of webs
14C21 Webs, nets

Keywords: linearizable web; linearization; maximal rank; web

Citations: Zbl 0483.53013; Zbl 0799.32010; Zbl 0386.14002; Zbl 0020.06701

Cited in: Zbl 0911.53008

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