Classification of Jets of Surfaces in Projective 3-Space Via Central Projection

  • H. Sano
  • Y. KabataEmail author
  • J. L. Deolindo Silva
  • T. Ohmoto


We present a local classification of smooth surfaces in \({\mathbb {P}}^3\) in terms of the singularity types (of codimension \(\le \)4) of their central projections to a plane. Based on our classification result, we also give exact normal forms to surface germs at transition moments on bifurcations with respect to parabolic curves and flecnodal curves.


Singularities of smooth maps Projection of surfaces Projective differential geometry 

Mathematics Subject Classification

Primary 58K05 Secondary 53A20 



The authors would like to thank Takashi Nishimira and Farid Tari for organizing the JSPS-CAPES international cooperation project in 2014-2015. In fact, the second and third authors are supported by the project for their stays in ICMC-USP and Hokkaido University, respectively. The authors appreciate Ricardo Uribe-Vargas for letting them take attention to his paper Uribe-Vargas (2002) and Panov’s (2000) and the referee for valuable comments in revising earlier versions of the present paper. The authors are partly supported by JSPS KAKENHI Grant Numbers 24340007 and 15K13452.


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Copyright information

© Sociedade Brasileira de Matemática 2017

Authors and Affiliations

  • H. Sano
    • 1
  • Y. Kabata
    • 3
    Email author
  • J. L. Deolindo Silva
    • 2
  • T. Ohmoto
    • 1
  1. 1.Department of Mathematics, Graduate School of ScienceHokkaido UniversitySapporoJapan
  2. 2.Departamento de Ciências Exatas e EducaçãoUniversidade Federal de Santa CatarinaBlumenauBrazil
  3. 3.Department of Mathematics, Graduate School of ScienceKobe UniversityKobeJapan

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