Sur l'algébrisation des tissus de rang maximal

Tissus algébriques exceptionnels

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.

Determination du rang des tissus du plan et autres invariants geometriques

Nous donnons un procede explicite de determination du rang d'un d-tissu non singulier du plan quelconque a l'aide de sa connexion associee. Une etude de quelques invariants du tissu est egalement proposee. We give an explicit process of determination of the rank of any non singular planar d-web thanks to its associated connection. A study of some invariants of the web is also proposed.

高阶数值域的凸代数几何

The convex algebraic geometry of higher-rank numerical ranges

本文研究高阶数值域的实代数与凸几何，推广 Kippenhahn 定理，并给出显式计算给定矩阵高阶数值域的算法。