Maximal Cohen-Macaulay Modules Over Non-Isolated Surface Singularities and Matrix Problems
Seiten
2017
American Mathematical Society (Verlag)
978-1-4704-2537-1 (ISBN)
American Mathematical Society (Verlag)
978-1-4704-2537-1 (ISBN)
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Develops a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, the authors give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay modules.
In this article the authors develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen-Macaulay representation type. The authors' approach is illustrated on the case of $/mathbb{k}[[ x,y,z]]/(xyz)$ 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 the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.
In this article the authors develop a new method to deal with maximal Cohen-Macaulay modules over non-isolated surface singularities. In particular, they give a negative answer on an old question of Schreyer about surface singularities with only countably many indecomposable maximal Cohen-Macaulay modules. Next, the authors prove that the degenerate cusp singularities have tame Cohen-Macaulay representation type. The authors' approach is illustrated on the case of $/mathbb{k}[[ x,y,z]]/(xyz)$ 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 the authors call representations of decorated bunches of chains. They prove that these matrix problems have tame representation type and describe the underlying canonical forms.
Igor Burban, Universitat zu Koln, Germany. Yuriy Drozd, National Academy of Sciences, Kyiv, Ukraine.
Generalities on maximal Cohen-Macaulay modules
Category of triples in dimension one
Main construction
Serre quotients and proof of Main Theorem
Singularities obtained by gluing cyclic quotient singularities
Maximal Cohen-Macaulay modules over $/mathbb{k}[[ x, y, z]]/(x^2 + y^3 - xyz)$
Representations of decorated bunches of chains-I
Maximal Cohen-Macaulay modules over degenerate cusps-I
Maximal Cohen-Macaulay modules over degenerate cusps-II
Schreyer's question
Remarks on rings of discrete and tame CM-representation type
Representations of decorated bunches of chains-II
References.
Erscheinungsdatum | 12.08.2017 |
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Reihe/Serie | Memoirs of the American Mathematical Society |
Verlagsort | Providence |
Sprache | englisch |
Maße | 178 x 254 mm |
Gewicht | 200 g |
Themenwelt | Mathematik / Informatik ► Mathematik ► Algebra |
Mathematik / Informatik ► Mathematik ► Geometrie / Topologie | |
ISBN-10 | 1-4704-2537-8 / 1470425378 |
ISBN-13 | 978-1-4704-2537-1 / 9781470425371 |
Zustand | Neuware |
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Buch | Softcover (2015)
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