Fröberg conjecture

In algebraic geometry, the Fröberg conjecture is a conjecture about the possible Hilbert functions of a set of forms. It is named after Ralf Fröberg, who introduced it in. The Fröberg–Iarrobino conjecture is a generalization introduced by.

Statement of Conjecture
Given generic homogeneous polynomials $$ g_1,g_2,\ldots,g_k\in \mathbb{C}[x_1,x_2,\ldots,x_n]$$of degrees $$ a_1,a_2,\ldots, a_k$$resp. Then the Hilbert Series of $$ \mathbb{C}[x_1,x_2,\ldots,x_n]/\langle g_1,g_2,\ldots, g_k\rangle $$is $$ {(1+t+t^2+\ldots)^n}{(1-t^{a_1})(1-t^{a_2})\cdots (1-t^{a_k})} $$ truncated at its first negative term.