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- W4384388184 abstract "Let $(S,mathfrak n)$ be a regular local ring and $f$ a non-zero element of $mathfrak n^2$. A theorem due to Knorrer states that there are finitely many isomorphism classes of maximal Cohen-Macaulay $R=S/(f)$-modules if and only if the same is true for the double branched cover of $R$, that is, the hypersurface ring defined by $f+z^2$ in $S[[ z ]]$. We consider an analogue of this statement in the case of the hypersurface ring defined instead by $f+z^d$ for $dge 2$. In particular, we show that this hypersurface, which we refer to as the $d$-fold branched cover of $R$, has finite Cohen-Macaulay representation type if and only if, up to isomorphism, there are only finitely many indecomposable matrix factorizations of $f$ with $d$ factors. As a result, we give a complete list of polynomials $f$ with this property in characteristic zero. Furthermore, we show that reduced $d$-fold matrix factorizations of $f$ correspond to Ulrich modules over the $d$-fold branched cover of $R$." @default.
- W4384388184 created "2023-07-15" @default.
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- W4384388184 date "2021-10-05" @default.
- W4384388184 modified "2023-10-17" @default.
- W4384388184 title "Branched covers and matrix factorizations" @default.
- W4384388184 doi "https://doi.org/10.1112/blms.12901" @default.
- W4384388184 hasPublicationYear "2021" @default.
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