Algebraic Cycles, Sheaves, Shtukas, and Moduli: Impanga Lecture Notes

ISBN-13: 9783764385361 / Angielski / Twarda / 2007 / 236 str.

Piotr Pragacz

Opis

Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski s contributions."

Spis treści

Notes on the Life and Work of Józef Maria Hoene-Wro?ski.- Exotic Fine Moduli Spaces of Coherent Sheaves.- Moduli Spaces of Coherent Sheaves on Multiples Curves.- Lectures on Principal Bundles over Projective Varieties.- Lectures on Torsion-free Sheaves and Their Moduli.- Miscellany on the Zero Schemes of Sections of Vector Bundles.- Thom Polynomials of Invariant Cones, Schur Functions and Positivity.- Geometric Invariant Theory Relative to a Base Curve.- Some Applications of Algebraic Cycles to Affine Algebraic Geometry.- to the Stacks of Shtukas.

Blurb

 

The articles in this volume are devoted to:

- moduli of coherent sheaves;

- principal bundles and sheaves and their moduli;

- new insights into Geometric Invariant Theory;

- stacks of shtukas and their compactifications;

- algebraic cycles vs. commutative algebra;

- Thom polynomials of singularities;

- zero schemes of sections of vector bundles.

The main purpose is to give "friendly" introductions to the above topics through a series of comprehensive texts starting from a very elementary level and ending with a discussion of current research. In these texts, the reader will find classical results and methods as well as new ones. The book is addressed to researchers and graduate students in algebraic geometry, algebraic topology and singularity theory. Most of the material presented in the volume has not appeared in books before.

 Contributors:

Jean-Marc Drézet, Tomás L. Gómez, Adrian Langer, Piotr Pragacz, Alexander H. W. Schmitt, Vasudevan Srinivas, Ngo Dac Tuan, Andrzej Weber