On conjectures of Itoh and of Lipman on the cohomology of normalized blow-ups
On conjectures of Itoh and of Lipman on the cohomology of normalized blow-ups
Let (R,𝔪,𝕜) be a three-dimensional Cohen–Macaulay analytically unramified local ring and I an 𝔪-primary R-ideal. Write X=Proj(⊕n∈ℕIn¯tn). We prove some consequences of the vanishing of H2(X,𝒪X), whose length equals the constant term e¯3(I) of the normal Hilbert polynomial of I. Firstly, X is Cohen–Macaulay. Secondly, if the extended Rees ring …