10 problems

Odd-degree annihilator correction conjecture. For odd $d>3$,

Initial-ideal containment conjecture. Then

For generic linear forms $l_i$, let … and let … Here $F_{n,r,d}(t)$ is the Hilbert series conjectured by Fröberg for generic degree-$d$ forms in the cases under consideration. The…

Generic quadratic Hilbert-series conjecture. For the indicated values of $n,r$, the following formulas hold:

Bigraded Fröberg conjecture. The Hilbert series of $R/(f_1,\ldots,f_r)$ is

Moreno-Socias's conjecture. The initial monomial ideal in degrevlex order of an ideal generated by generic forms is almost degrevlex.

Iarrobino's conjecture. Outside these exceptions, the algebras

Migliore–Miro-Roig conjecture. The minimal free resolution of $S/I$ has no redundant term. Consequently, the minimal free resolution is the minimum one consistent with the Hilbert…

Let $R=\mathbb{C}[x_1,\ldots,x_n]$, with $g_1,\ldots,g_k$ generic forms of degree $d\geq2$, and let $m\in\mathbb{N}$. Set … For a power series $F(t)$, write $\lceil F(t)\rceil$ for…

Let $S=\Bbbk[x_1,\ldots,x_n]$, let $J\subset S$ be generated by generic forms, and let $f\in S$ be a generic form of degree $e$. Recursive Fröberg conjecture. For every integer $j$…