Topics in Cohomological Studies of Algebraic Varieties

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

Expository treatment of the material Contains results on intersection theory on flag varieties that have not been published before Describes, for the first time in the literature of this type, the Richardson varieties and Grothendieck polynomials Contains many concrete examples which are very useful for the reader to study the theories presented

Inhalt
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.