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The articles in this volume study various cohomological aspects of algebraic varieties:
- characteristic classes of singular varieties;
- geometry of flag varieties;
- cohomological computations for homogeneous spaces;
- K-theory of algebraic varieties;
- quantum cohomology and Gromov-Witten theory.
The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before.
Contributors:
Paolo Aluffi
Michel Brion
Anders Skovsted Buch
Haibao Duan
Ali Ulas Ozgur Kisisel
Piotr Pragacz
Jörg Schürmann
Marek Szyjewski
Harry Tamvakis
List of contents
Characteristic Classes of Singular Varieties.- Lectures on the Geometry of Flag Varieties.- Combinatorial K-theory.- Morse Functions and Cohomology of Homogeneous Spaces.- Integrable Systems and Gromov-Witten Theory.- Multiplying Schubert Classes.- Lectures on Characteristic Classes of Constructible Functions.- Algebraic K-theory of Schemes.- Gromov-Witten Invariants and Quantum Cohomology of Grassmannians.
Summary
The articles in this volume study various cohomological aspects of algebraic varieties:
- characteristic classes of singular varieties;
- geometry of flag varieties;
- cohomological computations for homogeneous spaces;
- K-theory of algebraic varieties;
- quantum cohomology and Gromov-Witten theory.
The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before.
Contributors:
Paolo Aluffi
Michel Brion
Anders Skovsted Buch
Haibao Duan
Ali Ulas Ozgur Kisisel
Piotr Pragacz
Jörg Schürmann
Marek Szyjewski
Harry Tamvakis
Additional text
From the reviews:
“It is certainly a volume that should guide and influence those who plan to be perfect in acquiring a detailed education and review of the cohomological studies of algebraic varieties. In short, the volume not only simply commands a presence on every mathematical bookshelf but also belongs in the library of everyone wishing to stay better informed on cohomological theories. … And the references listed at the end of each contribution have a remarkable value for the intended readers.” (Current Engineering Practice, Vol. 48, 2005-2006)
