Logarithmic orbifold Euler numbers of surfaces with applications

Details Logarithmic orbifold Euler numbers of surfaces with applications Logarithmic orbifold Euler numbers of surfaces with applications

2000-12-19

arxiv.org/abs/math/0012180v1

Mathematics

Algebraic Geometry

37 pages; AMSTeX

Scientific paper

We introduce orbifold Euler numbers for normal surfaces with Q-divisors. These numbers behave multiplicatively under finite maps and in the log canonical case we prove that they satisfy the Bogomolov-Miyaoka-Yau type inequality. As a corollary we prove effective versions of Bogomolov's result on boundedness of rational curves in some surfaces of general type. Finally, we give some applications to singularities of plane curves.

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