## Osaka Journal of Mathematics

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

María Martí Sánchez

#### Abstract

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

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

Dates
First available in Project Euclid: 26 September 2011

https://projecteuclid.org/euclid.ojm/1317044941

Mathematical Reviews number (MathSciNet)
MR2837675

Zentralblatt MATH identifier
1229.14030

#### Citation

Martí Sánchez, María. Even sets of ($-4$)-curves on rational surface. Osaka J. Math. 48 (2011), no. 3, 675--690. https://projecteuclid.org/euclid.ojm/1317044941

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