Quadratic forms and singularities of genus one or two

Georges Dloussky[1]

  • [1] Centre de Mathématiques et d’Informatique, Université de Provence, 39 rue F. Joliot-Curie 13453 Marseille Cedex 13, France.

Annales de la faculté des sciences de Toulouse Mathématiques (2011)

  • Volume: 20, Issue: 1, page 15-69
  • ISSN: 0240-2963

Abstract

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We study singularities obtained by the contraction of the maximal divisor in compact (non-kählerian) 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 discriminants of the quadratic forms of these singularities. We introduce a multiplicative branch topological invariant which determines the twisting coefficient of a non-vanishing holomorphic 1-form on the complement of the singular point.

How to cite

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Dloussky, Georges. "Quadratic forms and singularities of genus one or two." Annales de la faculté des sciences de Toulouse Mathématiques 20.1 (2011): 15-69. <http://eudml.org/doc/219761>.

@article{Dloussky2011,
abstract = {We study singularities obtained by the contraction of the maximal divisor in compact (non-kählerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be $\mathbb\{Q\}$-Gorenstein, numerically Gorenstein or Gorenstein. A family of polynomials depending on the configuration of the curves computes the discriminants of the quadratic forms of these singularities. We introduce a multiplicative branch topological invariant which determines the twisting coefficient of a non-vanishing holomorphic 1-form on the complement of the singular point.},
affiliation = {Centre de Mathématiques et d’Informatique, Université de Provence, 39 rue F. Joliot-Curie 13453 Marseille Cedex 13, France.},
author = {Dloussky, Georges},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {minimal compact complex surfaces in class ; global spherical shells; singularities; -Gorenstein; numerically Gorenstein; twisting coefficient},
language = {eng},
month = {1},
number = {1},
pages = {15-69},
publisher = {Université Paul Sabatier, Toulouse},
title = {Quadratic forms and singularities of genus one or two},
url = {http://eudml.org/doc/219761},
volume = {20},
year = {2011},
}

TY - JOUR
AU - Dloussky, Georges
TI - Quadratic forms and singularities of genus one or two
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2011/1//
PB - Université Paul Sabatier, Toulouse
VL - 20
IS - 1
SP - 15
EP - 69
AB - We study singularities obtained by the contraction of the maximal divisor in compact (non-kählerian) surfaces which contain global spherical shells. These singularities are of genus 1 or 2, may be $\mathbb{Q}$-Gorenstein, numerically Gorenstein or Gorenstein. A family of polynomials depending on the configuration of the curves computes the discriminants of the quadratic forms of these singularities. We introduce a multiplicative branch topological invariant which determines the twisting coefficient of a non-vanishing holomorphic 1-form on the complement of the singular point.
LA - eng
KW - minimal compact complex surfaces in class ; global spherical shells; singularities; -Gorenstein; numerically Gorenstein; twisting coefficient
UR - http://eudml.org/doc/219761
ER -

References

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