Universität zu Köln

Burban, Igor and Drozd, Yuriy ORCID: 0000-0002-4766-8791 (2017). Generalities on maximal Cohen-Macaulay modules. Mem. Am. Math. Soc., 248 (1178). S. 1 - 116. PROVIDENCE: AMER MATHEMATICAL SOC. ISSN 1947-6221

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Abstract

In this article we develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, we give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay modules. Next, we prove that the degenerate cusp singularities have tame Cohen-Macaulay representation type. Our approach is illustrated on the case of k[x, y, z]/(xyz) as well as several other rings. This study of maximal Cohen-Macaulay modules over non-isolated 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.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Burban, Igor UNSPECIFIED UNSPECIFIED UNSPECIFIED Drozd, Yuriy UNSPECIFIED orcid.org/0000-0002-4766-8791 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-226720
DOI:	10.1090/memo/1178
Journal or Publication Title:	Mem. Am. Math. Soc.
Volume:	248
Number:	1178
Page Range:	S. 1 - 116
Date:	2017
Publisher:	AMER MATHEMATICAL SOC
Place of Publication:	PROVIDENCE
ISSN:	1947-6221
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language HOMOLOGICAL MIRROR SYMMETRY; DIMENSIONAL QUOTIENT SINGULARITIES; TRIANGULATED CATEGORIES; REFLEXIVE MODULES; CURVE SINGULARITIES; COHERENT SHEAVES; EQUATIONS; MUTATION; TAME Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/22672