English

Some classical formul{\ae} for curves and surfaces

Algebraic Geometry 2025-12-03 v2

Abstract

The goal of this text is to present the computation by Salmon, in the second half of the XIXth century, of various numbers enumerating planes with a prescribed tangency pattern with a sufficiently general surface SS in P3\mathbf{P}^3 (or, equivalently, of hyperplane sections of SS with prescribed singularities). Emblematic among these are the number of tritangent planes, and the number of planes cutting out a curve with a tacnode.

Keywords

Cite

@article{arxiv.2510.18686,
  title  = {Some classical formul{\ae} for curves and surfaces},
  author = {Thomas Dedieu},
  journal= {arXiv preprint arXiv:2510.18686},
  year   = {2025}
}

Comments

v2: minor improvements to the appendix on polarity

R2 v1 2026-07-01T06:58:00.284Z