Advertisement

Geometriae Dedicata

, Volume 120, Issue 1, pp 59–72 | Cite as

Desargues Configurations via Polar Conics of Plane Cubics

  • D. Avritzer
  • H. Lange
Article
  • 55 Downloads

Abstract

Using polar conics of plane cubics we define a rational map \(\Psi_m: \mathcal{M}_6^b \rightarrow \mathcal{M}_D\) from the moduli space of stable binary sextics into the moduli space of Desargues configurations. We show that this map is the inverse of a birational map \(\Phi_s: \mathcal{M}_D \rightarrow \mathcal{M}_6^b\) defined via the von Staudt conic. In particular Ψ m is a birational map.

Keywords

Desargues configuration moduli space of binary sextics 

Mathematics Subject Classifications (2000)

primary 51N35 secondary 14N05 51N15 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Avritzer D. and Lange H. (2002). Curves of genus 2 and Desargues configurations. Adv. Geom. 2:259–280zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Kantor S. (1881). Die Configurationen (3,3)10. Sitz. -Ber. Wiener Akad. Wiss. 84 2:1291–1314Google Scholar
  3. 3.
    Marr W. L. (1926). Polar properties of cubics through six points on a conic. J. Lond. Math. Soc. 1:86–93CrossRefGoogle Scholar
  4. 4.
    Marr W. L. (1930). Polar properties of cubics through six points on a conic. Additional note: A Desargues configuration of the poles. J. Lond. Math. Soc. 5:193–195Google Scholar
  5. 5.
    Stephanos, C.: Mémoires sur les faisceaux de formes binaires ayant une même jacobienne, Mém. Acad. Sci. Inst. National de France 27, Nr. 7, (1883).Google Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Departamento de MatemáticaUFMGBelo HorizonteBrazil
  2. 2.Mathematisches InstitutErlangenGermany

Personalised recommendations