CiNii 図書 - Isolated singular points on complete intersections

This book comprises five expository articles and two research papers on topics of current interest in set theory and the foundations of mathematics. Articles by Baumgartner and Devlin introduce the reader to proper forcing. This is a development by Saharon Shelah of Cohen's method which has led to solutions of problems that resisted attack by forcing methods as originally developed in the 1960s. The article by Guaspari is an introduction to descriptive set theory, a subject that has developed dramatically in the last few years. Articles by Kanamori and Stanley discuss one of the most difficult concepts in contemporary set theory, that of the morass, first created by Ronald Jensen in 1971 to solve the gap-two conjecture in model theory, assuming Goedel's axiom of constructibility. The papers by Prikry and Shelah complete the volume by giving the reader the flavour of contemporary research in set theory. This book will be of interest to graduate students and research workers in set theory and mathematical logic.

1. Iterated Forcing James E. Baumgartner
2. The Yorkshireman's guide to proper forcing Keith J. Devlin
3. The singular cardinals problem
independence results Sharon Shelah
4. Trees, norms and scales David Guaspari
5. On the regularity of ultrafilters Karel Prikry
6. Morasses in combinatorial set theory Akihiro Kanamori
7. A short course on gap-one morasses with a review of the fine structure of L Lee Stanley.

巻冊次: : pbk ISBN 9780521286749

内容説明

Singularity theory is not a field in itself, but rather an application of algebraic geometry, analytic geometry and differential analysis. The adjective 'singular' in the title refers here to singular points of complex-analytic or algebraic varieties or mappings. A tractable (and very natural) class of singularities to study are the isolated complete intersection singularities, and much progress has been made over the past decade in understanding these and their deformations.

1. Examples of isolated singular points
2. The milnor fibration
3. Picard-Lefschetz formulas
4. Critical space and discriminant space
5. Relative monodromy
6. Deformations
7. Vanishing lattices, monodromy groups and adjacency
8. The local Guass-Manin connection
9. Applications of the local Gauss-Manin connection.

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Isolated singular points on complete intersections

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