Betti strata of height two ideals
نویسنده
چکیده
Let R = k[x, y] denote the polynomial ring in two variables over an infinite field k. We study the Betti strata of the family G(H) parametrizing graded Artinian quotients of R = k[x, y] having given Hilbert function H . The Betti stratum Gβ(H) parametrizes all quotients A of having the graded Betti numbers determined by H and the minimal relation degrees β, with βi = dimk Tor R 1 (I, k)i. We recover that the Betti strata are irreducible, and we calculate their codimension in the family G(H). Theorem. The codimension of Gβ(H) in G(H) satisfies, letting νi = #{ generators of degree i}, and βi = #{ relations of degree i}, cod Gβ(H) = ∑
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