Tissus alg\'ebriques exceptionnels

TL;DR

This paper constructs examples of exceptional algebraic webs that have maximal rank but are not algebraizable in the classical sense, focusing on a specific case previously identified as an exception.

Contribution

It identifies and constructs new examples of exceptional algebraic webs in a specific parameter case, expanding understanding of web algebraizability.

Findings

Constructed examples of exceptional algebraic webs

Demonstrated existence of non-classically algebraizable webs with maximal rank

Focused on the case where d = (r+2)(n-1)+1 for n > 2

Abstract

In arXiv:1302.3142, it has been proved that for r>1, n>1 and d>(r+1)(n-1)+1, a d-web of type (r,n) with maximal rank is algebraizable in the classical sense, except maybe when n>2 and d = (r+2)(n-1)+1. In the present paper, one considers this particular case. Under these hypotheses on r, n and d, one constructs some examples of `exceptional algebraic webs': these are generalized algebraic webs of maximal rank that aren't algebraizable in the classical sense.