# About maximal Cohen-Macaulay modules

I´m trying to solve a problem of cancellation of reflexive finitely generated modules over normal noetherian domains. When $R$ is regular domain with $\dim R \le 2$, for finitely generated modules, reflexive is equivalent to projective.

Now I´m studying the case $\dim R=2$ and $R$ normal. In this hypothesis, reflexive modules are maximal Cohen-Macaulay modules.

I´m looking for references about this topic, with especial emphasis in lifting of homomorphism between factors of maximal CM modules: something like "... an homomorphism $M/IM\to N/IN$ can be lift to an homomorphism $M\to N...$"; indescomponibles maximal CM modules are welcome too.

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## 2 Answers

You probably want to look at this paper: http://www.springerlink.com/content/8r44x50448644568/

on deformations of MCM modules and the references there.

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It seems fine! thanks a lot! – Hideyuki Kabayakawa Dec 16 '09 at 19:42

This review seems perfect for your needs: Maximal Cohen-Macaulay modules over surface singularities (Burban, Drozd)

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¡Gracias! ¡Ya le había echado el ojo! – Hideyuki Kabayakawa Dec 16 '09 at 19:41