# When the positivity of the $$h$$h-vector implies the Cohen-Macaulay property

@article{Cioffi2012WhenTP, title={When the positivity of the \$\$h\$\$h-vector implies the Cohen-Macaulay property}, author={Francesca Cioffi and Roberta Di Gennaro}, journal={Ricerche di Matematica}, year={2012}, volume={63}, pages={195-209} }

We study relations between the Cohen-Macaulay property and the positivity of the $$h$$h-vector of a locally Cohen-Macaulay equidimensional closed subscheme $$X\subset {\mathbb {P}}^n_K$$X⊂PKn, showing that these two conditions are equivalent for those $$X$$X which are close to a complete intersection $$Y$$Y (of the same codimension) in terms of the difference between the degrees. More precisely, let $$X$$X be contained in $$Y$$Y, either of codimension two with $$deg(Y)-deg(X)\le 5$$deg(Y)-deg(X… Expand

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