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

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

2010-03-24

arxiv.org/abs/1003.4648v1

Mathematics

Algebraic Geometry

17 pages

Scientific paper

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.

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