Preprint No.
A0309
Georg Hein
On the effective cone of algebraic surfaces
Abstract:
The effective cone of an algebraic surface $X$
may contain infinitely many curves
of negative self intersection.
We show that at most $\max\{\rho(X)1, 2\rho(X)4 \}$ of these curves
can have trivial intersection with a given nontrivial
nef line bundle $L$.
Here $\rho(X)$ denotes the Picard number of $X$, i.e.,
the rank of the N\'eronSeveri group $\NS(X)$.
We end this article with upper bounds
for the number of reducible fibers of
surface fibrations over curves.
Keywords: Reducible fibre, algebraic surface, effective cone, nef line bundle
Mathematics Subject Classification (MSC2000):
14C22, 14D06
Language: ENG
Available: PrA0309.ps
Contact: Georg Hein, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 26, D14195 Berlin, Germany (ghein@math.fuberlin.de)
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Created: 20040121 