English

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.

Keywords

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

R2 v1 2026-07-22T17:51:10.613Z