Quadratic forms and singularities of genus one or two
Complex Variables
2008-01-07 v2 Algebraic Geometry
Abstract
We study singularities obtained by the contraction of the maximal divisor in compact (non kaehlerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be Q-Gorenstein, numerically Gorenstein or Gorenstein. A family of polynomials depending on the configuration of the curves computes the discriminant of the quadratic forms of these singularities. We introduce a multiplicative branch topological invariant which determines the twisting of a non-vanishing holomorphic 1-form on the complement of the singular point.
Cite
@article{arxiv.math/0702467,
title = {Quadratic forms and singularities of genus one or two},
author = {Georges Dloussky},
journal= {arXiv preprint arXiv:math/0702467},
year = {2008}
}
Comments
40 pages, 33 figures, misprints corrected, section 3.4 added