Portugaliae Mathematica   EMIS ELibM Electronic Journals PORTUGALIAE
Vol. 57, No. 1, pp. 59-95 (2000)

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Lines on Del Pezzo Surfaces with $K_{S}^{2}=1$ in Characteristic 2 in The Smooth Case

P. Cragnolini and P.A. Oliverio

Dip. di Matematica e Informatica, Università di Udine,
I-33100 Udine - ITALY
E-mail: cragno@dimi.uniud.it
Dip. di Matematica, Università della Calabria,
I-87036 Rende - ITALY
E-mail: oliverio@unical.it

Abstract: In the case when the branch divisor of the antibicanonical map is smooth, we prove the existence in characteristic $2$ of 240 $(-1)$-curves on a smooth projective surface with $q=0$, $K_{S}^{2}=1$, $|{-}K_{S}|$ ample and containing an irreducible reduced curve, concluding in this case the proof of Castelnuovo's criterion of rationality.

Keywords: Del Pezzo surface; $(-1)$-curve.

Classification (MSC2000): 14J26.

Full text of the article:

Electronic version published on: 31 Jan 2003. This page was last modified: 27 Nov 2007.

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