The Cohen-Macaulay representation type of arithmetically Cohen-Macaulay varieties

TL;DR

This paper classifies the Cohen-Macaulay representation types of arithmetically Cohen-Macaulay varieties, showing most are of wild type except for specific cases, which are fully characterized.

Contribution

It provides a complete classification of the Cohen-Macaulay representation types for arithmetically Cohen-Macaulay varieties, identifying the exceptional cases.

Findings

Most reduced closed subschemes with Cohen-Macaulay coordinate rings are of wild type.

A complete classification of the exceptional cases with non-wild type.

The paper delineates the boundary between wild and tame Cohen-Macaulay types.

Abstract

We show that all reduced closed subschemes of projective space that have a Cohen-Macaulay graded coordinate ring are of wild Cohen-Macaulay type, except for a few cases which we completely classify.