On the classification of Togliatti systems
Abstract
In [MeMR], Mezzetti and MiróRoig proved that the minimal number of generators $\mu (I)$ of a minimal (smooth) monomial Togliatti system $I\subset k[x_{0},\dotsc,x_{n}]$ satisfies $2n+1\le \mu(I)\le \binom{n+d1}{n1}$ and they classify all smooth minimal monomial Togliatti systems $I\subset k[x_{0},\dotsc,x_{n}]$ with $2n+1\le \mu(I)\le 2n+2$. In this paper, we address the first open case. We classify all smooth monomial Togliatti systems $I\subset k[x_{0},\dotsc,x_{n}]$ of forms of degree $d\ge 4$ with $\mu(I)=2n+3$ and $n\ge 2$ and all monomial Togliatti systems $I\subset k[x_0,x_1,x_2]$ of forms of degree $d\ge 6$ with $\mu(I)=7$.
 Publication:

arXiv eprints
 Pub Date:
 October 2017
 DOI:
 10.48550/arXiv.1710.03579
 arXiv:
 arXiv:1710.03579
 Bibcode:
 2017arXiv171003579M
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Commutative Algebra
 EPrint:
 To appear in Communications in Algebra. arXiv admin note: text overlap with arXiv:1506.05914