Overview

This text studies Hilbert schemes of zero-dimensional subschemes of smooth varieties and several related parameter varieties of interest in enumerative geometry. The main aim 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.

Full Product Details

Author:   Lothar Göttsche
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   1994 ed.
Volume:   1572
Dimensions:   Width: 15.50cm , Height: 1.10cm , Length: 23.50cm
Weight:   0.670kg
ISBN:  

9783540578147

ISBN 10:   3540578145
Pages:   202
Publication Date:   28 March 1994
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Fundamental facts.- Computation of the Betti numbers of Hilbert schemes.- The varieties of second and higher order data.- The Chow ring of relative Hilbert schemes of projective bundles.

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