When the positivity of the hvector implies the CohenMacaulay property
Abstract
We study relations between the CohenMacaulay property and the positivity of $h$vectors, showing that these two conditions are equivalent for those locally CohenMacaulay equidimensional closed projective subschemes $X$, which are close to a complete intersection $Y$ (of the same codimension) in terms of the difference between the degrees. More precisely, let $X\subset \mathbb P^n_K$ ($n\geq 4$) be contained in $Y$, either of codimension two with $deg(Y)deg(X)\leq 5$ or of codimension $\geq 3$ with $deg(Y)deg(X)\leq 3$. Over a field $K$ of characteristic 0, we prove that $X$ is arithmetically CohenMacaulay if and only if its $h$vector is positive, improving results of a previous work. We show that this equivalence holds also for space curves $C$ with $deg(Y)deg(C)\leq 5$ in every characteristic $ch(K)\neq 2$. Moreover, we find other classes of subschemes for which the positivity of the $h$vector implies the CohenMacaulay property and provide several examples.
 Publication:

arXiv eprints
 Pub Date:
 December 2012
 arXiv:
 arXiv:1212.0989
 Bibcode:
 2012arXiv1212.0989C
 Keywords:

 Mathematics  Algebraic Geometry;
 14M05;
 14M06;
 14M10
 EPrint:
 Main changes with respect the previuos version are in the title, the abstract, the introduction and the bibliography