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OverviewModuli 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. Full Product DetailsAuthor: Oscar ZariskiPublisher: American Mathematical Society Imprint: American Mathematical Society Edition: illustrated edition Volume: No. 39 Weight: 0.304kg ISBN: 9780821829837ISBN 10: 0821829831 Pages: 151 Publication Date: 30 December 2006 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Table of ContentsPreliminaries Equisingularity invariants Parametrizations The moduli space Examples Applications of deformation theory Bibliography Appendix.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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