Moduli Problem for Plane Branches (University Lecture Series) - Softcover

American Mathematical Society

 
9780821829837: Moduli Problem for Plane Branches (University Lecture Series)
Softcover
ISBN 10: 0821829831 ISBN 13: 9780821829837
Publisher: American Mathematical Society, 2007

Synopsis

Moduli problems in algebraic geometry date back to Riemann's famous count of the $3g-3$ parameters needed to determine a curve of genus $g$. In this book, Zariski studies the moduli space of curves of the same equisingularity class. After setting up and reviewing the basic material, Zariski devotes one chapter to the topology of the moduli space, including an explicit determination of the rare cases when the space is compact. Chapter V looks at specific examples where the dimension of the generic component can be determined through rather concrete methods. Zariski's last chapter concerns the application of deformation theory to the moduli problem, including the determination of the dimension of the generic component for a particular family of curves. An appendix by Bernard Teissier reconsiders the moduli problem from the point of view of deformation theory. He gives new proofs of some of Zariski's results, as well as a natural construction of a compactification of the moduli space.

"synopsis" may belong to another edition of this title.

Publisher
American Mathematical Society
Publication date
2007
Language
English
ISBN 10 
0821829831
ISBN 13 
9780821829837
Binding
Paperback
Number of pages
151