Projective surfaces with many skew lines

Rams, Sławomir

doi:10.1090/S0002-9939-04-07519-7

Projective surfaces with many skew lines
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by Sławomir Rams PDF

Proc. Amer. Math. Soc. 133 (2005), 11-13 Request permission

Abstract:

We give an example of a smooth surface $\mathrm {S}_{d}\subset \mathbb {P}_{3}(\mathbb {C})$ of degree $d$ that contains $d \cdot (d-2) + 2$ pairwise disjoint lines. In particular, our example shows that the degree in Miyaoka’s bound is sharp.

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