1,664 research outputs found
The Orevkov invariant of an affine plane curve
We show that although the fundamental group of the complement of an algebraic
affine plane curve is not easy to compute, it possesses a more accessible
quotient, which we call the Orevkov invariant.Comment: 20 page
Complete intersection singularities of splice type as universal abelian covers
It has long been known that every quasi-homogeneous normal complex surface
singularity with Q-homology sphere link has universal abelian cover a Brieskorn
complete intersection singularity. We describe a broad generalization: First,
one has a class of complete intersection normal complex surface singularities
called "splice type singularities", which generalize Brieskorn complete
intersections. Second, these arise as universal abelian covers of a class of
normal surface singularities with Q-homology sphere links, called
"splice-quotient singularities". According to the Main Theorem,
splice-quotients realize a large portion of the possible topologies of
singularities with Q-homology sphere links. As quotients of complete
intersections, they are necessarily Q-Gorenstein, and many Q-Gorenstein
singularities with Q-homology sphere links are of this type. We conjecture that
rational singularities and minimally elliptic singularities with Q-homology
sphere links are splice-quotients. A recent preprint of T Okuma presents
confirmation of this conjecture.Comment: Published by Geometry and Topology at
http://www.maths.warwick.ac.uk/gt/GTVol9/paper17.abs.htm
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