Componentwise Linear Ideals with Minimal or Maximal Betti Numbers
نویسندگان
چکیده
We characterize componentwise linear monomial ideals with minimal Taylor resolution and consider the lower bound for the Betti numbers of componentwise linear ideals. INTRODUCTION Let S = K[x1, . . . ,xn] denote the polynomial ring in n variables over a field K with each degxi = 1. Let I be a monomial ideal of S and G(I) = {u1, . . . ,us} its unique minimal system of monomial generators. The Taylor resolution [4, p. 439] provides a graded free resolution of S/I. Fröberg [6, Proposition 1] characterizes the monomial ideals for which the Taylor resolution is minimal. In most cases it is indeed not minimal, however it yields the following upper bound for the Betti numbers of I. βi(I) ≤ (
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