# Bounding invariants of fat points using a coding theory construction Academic Article

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### abstract

• 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.

### publication date

• February 2013