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 Template:Ill, who introduced it in Template:Harvs. The Fröberg–Iarrobino conjecture is a generalization introduced by Template:Harvs.

Statement of Conjecture

Given generic homogeneous polynomials $g_1,g_2,\dots ,g_k\in ℂ[x_1,x_2,\dots ,x_n]$ of degrees $a_1,a_2,\dots ,a_k$, respectively. Then the Hilbert series of $ℂ[x_1,x_2,\dots ,x_n]/⟨g_1,g_2,\dots ,g_k⟩$ is

$(1+t+t^2+\cdots {)}^n(1-t^{a_1})(1-t^{a_2})\cdots (1-t^{a_k}),$

truncated at its first negative term.

References

• Template:Citation
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