Resumen de The dimension of certain catalecticant varieties

Aldo Conca , Giuseppe Valla

• Let $V_{s,t}$ be the rank $\leq s$ locus in $\mathbb{P}^{{2t+2\choose 2 }-1}$ of the generic catalecticant matrix Cat$(t, t; 3)$. This matrix has rather more symmetry than a generic symmetric matrix; this implies codim $Vs,t\leq{\widetilde s+1\choose 2}$, where $\widetilde s:= {t+2\choose 2}-s$. In this paper, given the integer $t$, we explicitely determine an integer $N$, depending on $t$, with the property that codim $Vs,t = {\widetilde s+1\choose 2}$ if and only if $\widetilde s\leq N$.