Maximal Cohen–Macaulay modules over surface singularities

  • Igor Burban

    Universität zu Köln, Germany
  • Yuriy Drozd

    National Academy of Science of Ukraine, Kyiv, Ukraine
Maximal Cohen–Macaulay modules over   surface  singularities cover
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Abstract

This is a survey article about properties of Cohen–Macaulay modules over surface singularities. We discuss results on the Macaulayfication functor, reflexive modules over simple, quotient and minimally elliptic singularities, geometric and algebraic McKay correspondence. Finally, we describe matrix factorizations corresponding to indecomposable Cohen–Macaulay modules over the non-isolated singularities A∞ and D∞.