Des s\'eries de tissus ordinaires de rang maximum en toute dimension

TL;DR

This paper introduces a method to define and verify properties of holomorphic webs of maximum rank in any dimension using a finite set of conditions, which can be checked efficiently with computer assistance.

Contribution

It establishes finite criteria for all such webs to be ordinary and of maximal rank, enabling practical verification via computer algorithms.

Findings

Finite conditions suffice to determine web properties.

Computer implementation allows efficient verification.

Applicable in any dimension for holomorphic webs.

Abstract

In this paper, we define, from a finite set E of functions, a family of holomorphic webs ${\cal W}(n;E)$ of codimension one in any dimension $ n $. We prove that it is sufficient to check a finite number of conditions for these webs to be all ordinary and to have all maximal rank. Moreover, these conditions may be practically checked by computer with the program on Maple published in [DL](arXiv1408.3909v1, DG, 18 August 2014), the time of computation being acceptable, as far as some integer $k_0$ given in the data be "not too big".