Hilbert Schemes of Zero-Dimensional Subschemes of Smooth Varieties

1994
ISBN: 978-3-540-57814-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 202 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 330 g

Reihe: Mathematisches Institut der Universität und Max-Planck-Institut für Mathematik, Bonn

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.

Zielgruppe

Research

Autoren/Hrsg.

Göttsche, Lothar

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie

Inhaltsverzeichnis

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.