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Hilbert Schemes of Zero-Dimensional Subschemes of Smooth Varieties

  • Book
  • © 1994

Overview

Authors:
  1. Lothar Göttsche
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1572)

Part of the book sub series: Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn (LNMMATH)

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Table of contents (4 chapters)

  1. Front Matter

    Pages I-IX
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  2. Fundamental facts

    • Lothar Göttsche
    Pages 1-11

  3. Computation of the Betti numbers of Hilbert schemes

    • Lothar Göttsche
    Pages 12-80

  4. The varieties of second and higher order data

    • Lothar Göttsche
    Pages 81-144

  5. The Chow ring of relative Hilbert schemes of projective bundles

    • Lothar Göttsche
    Pages 145-183

  6. Back Matter

    Pages 184-198
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Keywords

About this book

In this book we study Hilbert schemes of zero-dimensional subschemes of smooth varieties and several related parameter varieties of interest in enumerative geometry. The main aim here is to describe their cohomology and Chow rings. Some enumerative applications are also given. The Weil conjectures are used to compute the Betti numbers of many of the varieties considered, thus also illustrating how this powerful tool can be applied. The book is essentially self-contained, assuming only a basic knowledge of algebraic geometry; it is intended both for graduate students and research mathematicians interested in Hilbert schemes, enumertive geometry and moduli spaces.

Bibliographic Information

  • Book Title: Hilbert Schemes of Zero-Dimensional Subschemes of Smooth Varieties

  • Authors: Lothar Göttsche

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0073491

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1994

  • Softcover ISBN: 978-3-540-57814-7Published: 28 March 1994

  • eBook ISBN: 978-3-540-48338-0Published: 15 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 202

  • Topics: Algebraic Geometry

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