[Turkmath:7251] Bogazici Matematik Carsamba Seminerleri - ilan ekte

[ferit.ozturk at boun.edu.tr]

Geçmiþ/gelecek konuþmalar için:
http://www.math.boun.edu.tr/index.php?option=com_content&task=section&id=49&Itemid=405
Konuþmalar Ýngilizce yapýlmaktadýr.


A short introduction to Lefschetz theory on the topology of algebraic varieties

Christophe Eyral
Aarhus University

Date : Wednesday, October 20, 2010
Time: 14:00
Place: TB 250, Bogazici Universitesi

Abstract: In his book ‘L’analysis situs et la géométrie
algébrique’, S. Lefschetz proved two
essential results on the topology of algebraic varieties: the Hyperplane
Section
Theorem and so-
called Second Lefschetz Theorem. These results give a comparison between the
homology groups
of a non-singular irreducible projective variety X in CP^n and the homology
groups of a generic
hyperplane section of X. Precisely, the Hyperplane Section Theorem says that,
for a generic hyper-
plane L, the natural map H_q (L ∩ X) → H_q (X)
is an isomorphism for q ≤ dim X − 2 and an epimorphism for q = dim
X
− 1. The Second Lefschetz
Theorem describes the kernel of the map H_{dim X−1} (L ∩ X) →
H_{dim X−1} (X)
in terms of vanishing cycles that appear in a generic pencil of hyperplanes. In
this talk, I will
discuss generalization of these theorems to quasi-projective varieties and
homotopy groups.

Tea and coffee will be served at 15:00
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