PORTUGALIAEMATHEMATICA
Vol. 57, No. 1, pp. 59-95 (2000)
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PORTUGALIAE MATHEMATICA 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 CaseP. Cragnolini and P.A. OliverioDip. 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.
© 2000 Sociedade Portuguesa de Matemática
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