Osaka Journal of Mathematics

Even sets of ($-4$)-curves on rational surface

María Martí Sánchez

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We study rational surfaces having an even set of disjoint ($-4$)-curves. The properties of the surface $S$ obtained by considering the double cover branched on the even set are studied. It is shown, that contrarily to what happens for even sets of ($-2$)-curves, the number of curves in an even set of ($-4$)-curves is bounded (less or equal to 12). The surface $S$ has always Kodaira dimension bigger or equal to zero and the cases of Kodaira dimension zero and one are completely characterized. Several examples of this situation are given.

Article information

Osaka J. Math., Volume 48, Number 3 (2011), 675-690.

First available in Project Euclid: 26 September 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14J26: Rational and ruled surfaces 14J17: Singularities [See also 14B05, 14E15]


Martí Sánchez, María. Even sets of ($-4$)-curves on rational surface. Osaka J. Math. 48 (2011), no. 3, 675--690.

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