Bounding invariants of fat points using a coding theory construction

Details Bounding invariants of fat points using a coding theory construction Bounding invariants of fat points using a coding theory construction

2011-08-05

arxiv.org/abs/1108.1359v2

Mathematics

Commutative Algebra

18 pages, 1 figure; accepted in J. Pure Appl. Algebra

Scientific paper

Let $Z \subseteq \proj{n}$ be a fat points scheme, and let $d(Z)$ be the minimum distance of the linear code constructed from $Z$. We show that $d(Z)$ imposes constraints (i.e., upper bounds) on some specific shifts in the graded minimal free resolution of $I_Z$, the defining ideal of $Z$. We investigate this relation in the case that the support of $Z$ is a complete intersection; when $Z$ is reduced and a complete intersection we give lower bounds for $d(Z)$ that improve upon known bounds.

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