Geometry of varieties for graded maximal Cohen–Macaulay modules


We study a variety for graded maximal Cohen–Macaulay modules, which was introduced by Dao and Shipman. The main result of this paper asserts that there are only a finite number of isomorphism classes of graded maximal Cohen–Macaulay modules with fixed Hilbert series over Cohen–Macaulay algebras of graded countable representation type.

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The author express his deepest gratitude to Yuji Yoshino for valuable discussions and helpful comments. The author also thank the referee for his/her careful reading and helpful comments that have improved the paper.

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Correspondence to Naoya Hiramatsu.

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Dedicated to Professor Yuji Yoshino on the occasion of his retirement

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The author was supported by JSPS KAKENHI Grant Number 18K13399.

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Hiramatsu, N. Geometry of varieties for graded maximal Cohen–Macaulay modules. manuscripta math. (2021).

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Mathematics Subject Classification

  • Primary: 13C14
  • Secondary: 16G60