A note on Froberg's conjecture for forms of equal degrees

作者：Nenashev Gleb^*

来源：Comptes Rendus Mathematique, 2017, 355(3): 272-276.

DOI：10.1016/j.crma.2017.01.011

In this note we study ideals generated by generic forms in polynomial rings over any algebraicly closed field of characteristic zero. We prove for many cases that the (d + k)-th graded component of an ideal generated by generic forms of degree d has the expected dimension (given by dimension count). And as a consequence of our result, we obtain that ideals generated by several generic forms of degrees d usually have the expected Hilbert series. The precise form of this expected Hilbert series, in general, is known as Freberg's conjecture.

• 出版日期2017-3