文档介绍：Lectures on
Results on Bezout’s Theorem
By
W. Vogel
Tata Institute of Fundamental Research
Bombay
1984
Lectures on
Results on Bezout’s Theorem
By
W. Vogel
Notes by
. Patil
Published for the
Tata Institute of Fundamental Research
Springer-Verlag
Berlin Heidelberg New York Tokyo
1984
Author
W. Vogel
Martin-Luther Universit¨at
Sektion Mathematik
DDR-401 Halle
Universit¨ats-platz 6
German Democratic Republic
©Tata Institute of Fundamental Research. 1984
ISBN 3-540-12679-1 Springer-Verlag, Berlin. Heidelberg.
New York. Tokyo
ISBN 0-387-12679-1 Springer-Verlag, New York. Heidelberg.
Berlin. Tokyo
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. Joshi at The Book Centre Limited,
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Introduction
These notes are based on a series of lectures given at the Tata Institute
in November and December, 1982. The lectures are centered about my
joint work with J¨urgen St¨uckrad [85] on an algebraic approach to the
intersection theory. More-over, chapter II and III also contain new re-
sults.
Today, we have the remarkable theory of and R. Mac-
person on defining algebraic intersections:
Suppose V and W are subvarieties of dimension v and w of a non-
singular algebraic variety X of dimension n. Then the equivalence class
V · W of algebraic v + w − n cycles which represents the algebraic inter-
section of V and W is defined up to rational equivalence in X. This inter-
section theory produces subvarieties Yi of V ∩ W, cycle classes αi on Yi,
positive integers mi, with miαi representing V ·W, and deg αi ≥ deg Yi
even in the case dim(V ∩ PW) , v + w − n.
Our object here is to give an algebraic approach to the intersection
theory b