On Auslander Modules of Normal Surface Singularities
Author: Kurt Behnke
Publisher:
Published: 1988
Total Pages: 19
ISBN-13:
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Author: Kurt Behnke
Publisher:
Published: 1988
Total Pages: 19
ISBN-13:
DOWNLOAD EBOOKAuthor: Kurt Behnke
Publisher:
Published: 1988
Total Pages: 38
ISBN-13:
DOWNLOAD EBOOKAuthor: Javier Fernández de Bobadilla
Publisher: American Mathematical Society
Published: 2024-07-25
Total Pages: 110
ISBN-13: 1470470535
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Author: András Némethi
Publisher: Springer Nature
Published: 2022-10-07
Total Pages: 732
ISBN-13: 3031067533
DOWNLOAD EBOOKThis monograph provides a comprehensive introduction to the theory of complex normal surface singularities, with a special emphasis on connections to low-dimensional topology. In this way, it unites the analytic approach with the more recent topological one, combining their tools and methods. In the first chapters, the book sets out the foundations of the theory of normal surface singularities. This includes a comprehensive presentation of the properties of the link (as an oriented 3-manifold) and of the invariants associated with a resolution, combined with the structure and special properties of the line bundles defined on a resolution. A recurring theme is the comparison of analytic and topological invariants. For example, the Poincaré series of the divisorial filtration is compared to a topological zeta function associated with the resolution graph, and the sheaf cohomologies of the line bundles are compared to the Seiberg–Witten invariants of the link. Equivariant Ehrhart theory is introduced to establish surgery-additivity formulae of these invariants, as well as for the regularization procedures of multivariable series. In addition to recent research, the book also provides expositions of more classical subjects such as the classification of plane and cuspidal curves, Milnor fibrations and smoothing invariants, the local divisor class group, and the Hilbert–Samuel function. It contains a large number of examples of key families of germs: rational, elliptic, weighted homogeneous, superisolated and splice-quotient. It provides concrete computations of the topological invariants of their links (Casson(–Walker) and Seiberg–Witten invariants, Turaev torsion) and of the analytic invariants (geometric genus, Hilbert function of the divisorial filtration, and the analytic semigroup associated with the resolution). The book culminates in a discussion of the topological and analytic lattice cohomologies (as categorifications of the Seiberg–Witten invariant and of the geometric genus respectively) and of the graded roots. Several open problems and conjectures are also formulated. Normal Surface Singularities provides researchers in algebraic and differential geometry, singularity theory, complex analysis, and low-dimensional topology with an invaluable reference on this rich topic, offering a unified presentation of the major results and approaches.
Author: Idun Reiten
Publisher: American Mathematical Soc.
Published: 1998
Total Pages: 216
ISBN-13: 9780821808504
DOWNLOAD EBOOKSurveys developments in the representation theory of finite dimensional algebras and related topics in seven papers illustrating different techniques developed over the recent years. For graduate students and researchers with a background in commutative algebra, including rings, modules, and homological algebra. Suitable as a text for an advanced graduate course. No index. Member prices are $31 for institutions and $23 for individuals, and are available to members of the Canadian Mathematical Society. Annotation copyrighted by Book News, Inc., Portland, OR
Author: Henning Krause
Publisher: Birkhäuser
Published: 2012-12-06
Total Pages: 437
ISBN-13: 3034884265
DOWNLOAD EBOOKThis book is concerned with the role played by modules of infinite length when dealing with problems in the representation theory of groups and algebras, but also in topology and geometry; it shows the intriguing interplay between finite and infinite length modules.
Author: Sergei D. Silvestrov
Publisher: Springer Science & Business Media
Published: 2008-11-18
Total Pages: 308
ISBN-13: 3540853324
DOWNLOAD EBOOKThis book explores the cutting edge of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics.
Author: Andrzej Skowroński
Publisher: European Mathematical Society
Published: 2008
Total Pages: 732
ISBN-13: 9783037190623
DOWNLOAD EBOOKThis book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.
Author: Igor Burban
Publisher: American Mathematical Soc.
Published: 2017-07-13
Total Pages: 134
ISBN-13: 1470425378
DOWNLOAD EBOOKIn 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 k 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.
Author: Vincent Cossart
Publisher: Springer
Published: 2006-11-14
Total Pages: 138
ISBN-13: 3540391258
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