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.
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equisingularity class, constant semigroup deformation, nonexact differential, isomorphic branches, miniversal deformation, plane branch, canonical parametrization, quadratic transform, moduli space, virtual multiplicities, analytic invariant, complete intersection, analytic type, integral closure, generic fiber, generic component, fraction field Key Phrases - Capitalized Phrases (CAPs): (learn more)
Eqs Defr, Product Decomposition Theorem, Nakayama's Lemma, Zariski's Course Browse Sample Pages:
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equisingularity class, constant semigroup deformation, nonexact differential, isomorphic branches, miniversal deformation, plane branch, canonical parametrization, quadratic transform, moduli space, virtual multiplicities, analytic invariant, complete intersection, analytic type, integral closure, generic fiber, generic component, fraction field Key Phrases - Capitalized Phrases (CAPs): (learn more)
Eqs Defr, Product Decomposition Theorem, Nakayama's Lemma, Zariski's Course Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Back Cover | Surprise Me!
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