Dong-Ming Zhang

Fr\"oberg's Conjecture for Quintics and Septics in Four Variables

Let $k$ be a field of characteristic zero and let $S=k[x_1,x_2,x_3,x_4]$. We prove Fr\"oberg's predicted Hilbert series for ideals generated by $r$ general forms of equal degree $d$ for every $r\geq1$ in each of the two cases $d=5$ and $d=7$. Relative to the classical cases $r\leq5$ and the equal-degree theorem through...