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.
Best Answer
You probably want to look at this paper: http://www.springerlink.com/content/8r44x50448644568/
on deformations of MCM modules and the references there.