Lower Bounds for Betti Numbers of Monomial Ideals

الأصل · EN

Let I be a monomial ideal of height c in a polynomial ring S over a field k. If I is not generated by a regular sequence, then we show that the sum of the betti numbers of S/I is at least 2ᶜ + 2ᶜ⁻¹ and characterize when equality holds. Lower bounds for the individual betti numbers are given as well.