Constructions of singular rational surfaces of Picard number one with ample canonical divisor

Details Constructions of singular rational surfaces of Picard number one with ample canonical divisor Constructions of singular rational surfaces of Picard number one with ample canonical divisor

2010-07-12

arxiv.org/abs/1007.1936v1

Mathematics

Algebraic Geometry

13 pages, 7 figures

Scientific paper

Koll\'ar gave a series of examples of rational surfaces of Picard number $1$ with ample canonical divisor having cyclic singularities. In this paper, we construct several series of new examples in a geometric way, i.e., by blowing up several times inside a configuration of curves on the projective plane and then by contracting chains of rational curves. One series of our examples have the same singularities as Koll\'ar's examples.

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