How to Order

For AMS eBook frontlist subscriptions or backfile collection purchases:

   1a. To purchase any ebook backfile or to subscibe to the current year of Contemporary Mathematics, please download this required license agreement,

   1b. To subscribe to the current year of Memoirs of the AMS, please download this required license agreement.

   2. Complete and sign the license agreement.

   3. Email, fax, or send via postal mail to:

Customer Services
American Mathematical Society
201 Charles Street Providence, RI 02904-2213  USA
Phone: 1-800-321-4AMS (4267)
Fax: 1-401-455-4046

Visit the AMS Bookstore for individual volume purchases.

Browse the current eBook Collections price list

Powered by MathJax
  Remote Access

Maximal Cohen–Macaulay Modules Over Non–Isolated Surface Singularities and Matrix Problems

About this Title

Igor Burban and Yuriy Drozd

Publication: Memoirs of the American Mathematical Society
Publication Year: 2017; Volume 248, Number 1178
ISBNs: 978-1-4704-2537-1 (print); 978-1-4704-4058-9 (online)
Published electronically: March 16, 2017
Keywords:Maximal Cohen–Macaulay modules, matrix factorizations, non–isolated surface singularities, degenerate cusps, tame matrix problems

View full volume PDF

View other years and numbers:

Table of Contents


  • Introduction, motivation and historical remarks
  • Chapter 1. Generalities on maximal Cohen–Macaulay modules
  • Chapter 2. Category of triples in dimension one
  • Chapter 3. Main construction
  • Chapter 4. Serre quotients and proof of Main Theorem
  • Chapter 5. Singularities obtained by gluing cyclic quotient singularities
  • Chapter 6. Maximal Cohen–Macaulay modules over $\kk \llbracket x, y, z\rrbracket /(x^2 + y^3 - xyz)$
  • Chapter 7. Representations of decorated bunches of chains–I
  • Chapter 8. Maximal Cohen–Macaulay modules over degenerate cusps–I
  • Chapter 9. Maximal Cohen–Macaulay modules over degenerate cusps–II
  • Chapter 10. Schreyer’s question
  • Chapter 11. Remarks on rings of discrete and tame CM–representation type
  • Chapter 12. Representations of decorated bunches of chains–II


In this article we develop a new method to deal with maximal CohenâĂŞMacaulay modules over nonâĂŞisolated surface singularities. In particular, we give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal CohenâĂŞMacaulay modules. Next, we prove that the degenerate cusp singularities have tame CohenâĂŞMacaulay representation type. Our approach is illustrated on the case of as well as several other rings. This study of maximal CohenâĂŞMacaulay modules over nonâĂŞisolated singularities leads to a new class of problems of linear algebra, which we call representations of decorated bunches of chains. We prove that these matrix problems have tame representation type and describe the underlying canonical forms.

References [Enhancements On Off] (What's this?)