Maximal Cohen-Macaulay modules over non-isolated surface singularities and matrix problems / Igor Burban and Yuriy Drozd.

By:

Burban, Igor [author]

Contributor(s):

Drozd, Yuriy [author]

Material type: Text

TextSeries: Memoirs of the American Mathematical Society ; v 248, no 1178.Publication details: Providence : American Mathematical Society, 2017.Description: xiv, 114 pages : illustrations ; 26 cmISBN:

9781470425371 (pbk. : alk. paper)

Subject(s):

DDC classification:

510 23 Am512

Contents:

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 k[x,y,z]/(x p2 s+y p3 s-xyz) -- 7. Representations of decorated bundles of chans - 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 chans - II.

Summary: 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.

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Item type	Current library	Call number	Status	Date due	Barcode	Item holds
Books	ISI Library, Kolkata	510 Am512 (Browse shelf(Opens below))	Available		138220

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"Volume 248, number 1178 (fourth of 5 numbers), July 2017."

Includes bibliographical references.

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 k[x,y,z]/(x p2 s+y p3 s-xyz) --
7. Representations of decorated bundles of chans - 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 chans - II.

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.

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