Preprint No. A-03-09

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\'eron-Severi 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


Contact: Georg Hein, Freie Universität Berlin, Fachbereich Mathematik und Informatik, Arnimallee 2-6, D-14195 Berlin, Germany (

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