| eBook ISBN: | 978-1-4704-4058-9 |
| Product Code: | MEMO/248/1178.E |
| List Price: | $75.00 |
| MAA Member Price: | $67.50 |
| AMS Member Price: | $45.00 |
| eBook ISBN: | 978-1-4704-4058-9 |
| Product Code: | MEMO/248/1178.E |
| List Price: | $75.00 |
| MAA Member Price: | $67.50 |
| AMS Member Price: | $45.00 |
-
Book DetailsMemoirs of the American Mathematical SocietyVolume: 248; 2017; 114 ppMSC: Primary 16; 13
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.
-
Table of Contents
-
Chapters
-
Introduction, motivation and historical remarks
-
1. Generalities on maximal Cohen–Macaulay modules
-
2. Category of triples in dimension one
-
3. Main construction
-
4. Serre quotients and proof of Main Theorem
-
5. Singularities obtained by gluing cyclic quotient singularities
-
6. Maximal Cohen–Macaulay modules over $\mathbb {k}\lBrack x, y, z\rBrack /(x^2 + y^3 - xyz)$
-
7. Representations of decorated bunches of chains–I
-
8. Maximal Cohen–Macaulay modules over degenerate cusps–I
-
9. Maximal Cohen–Macaulay modules over degenerate cusps–II
-
10. Schreyer’s question
-
11. Remarks on rings of discrete and tame CM–representation type
-
12. Representations of decorated bunches of chains–II
-
-
Additional Material
-
RequestsReview Copy – for publishers of book reviewsPermission – for use of book, eBook, or Journal contentAccessibility – to request an alternate format of an AMS title
- Book Details
- Table of Contents
- Additional Material
- Requests
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.
-
Chapters
-
Introduction, motivation and historical remarks
-
1. Generalities on maximal Cohen–Macaulay modules
-
2. Category of triples in dimension one
-
3. Main construction
-
4. Serre quotients and proof of Main Theorem
-
5. Singularities obtained by gluing cyclic quotient singularities
-
6. Maximal Cohen–Macaulay modules over $\mathbb {k}\lBrack x, y, z\rBrack /(x^2 + y^3 - xyz)$
-
7. Representations of decorated bunches of chains–I
-
8. Maximal Cohen–Macaulay modules over degenerate cusps–I
-
9. Maximal Cohen–Macaulay modules over degenerate cusps–II
-
10. Schreyer’s question
-
11. Remarks on rings of discrete and tame CM–representation type
-
12. Representations of decorated bunches of chains–II
