English

The Poincar\'{e} series of some special quasihomogeneous surface singularities

Algebraic Geometry 2007-05-23 v3 Mathematical Physics Commutative Algebra math.MP

Abstract

In the author's paper ''Poincar\'{e} series and monodromy of a two-dimensional quasihomogeneous hypersurface singularity'' a relation is proved between the Poincar\'{e} series of the coordinate algebra of a two-dimensional quasihomogeneous isolated hypersurface singularity and the characteristic polynomial of its monodromy operator. We study this relation for Fuchsian singularities and show that it is connected with the mirror symmetry of K3 surfaces and with automorphisms of the Leech lattice. We also indicate relations between other singularities and Conway's group.

Keywords

Cite

@article{arxiv.math/0004086,
  title  = {The Poincar\'{e} series of some special quasihomogeneous surface singularities},
  author = {Wolfgang Ebeling},
  journal= {arXiv preprint arXiv:math/0004086},
  year   = {2007}
}

Comments

LaTeX2e, 17 pages, 2 figures; rewritten; only part of the old preprint; other part rewritten as ''Poincar\'{e} series and monodromy of a two-dimensional quasihomogeneous hypersurface singularity''