Segre's theorem on ovals in Desarguesian projective planes

Autor:	Browne, Patrick J., Dougherty, Steven T., Catháin, Padraig Ó
Rok vydání:	2023
Předmět:	Mathematics - Combinatorics Mathematics - Algebraic Geometry Mathematics - History and Overview 51E21
Druh dokumentu:	Working Paper
Popis:	Segre's theorem on ovals in projective spaces is an ingenious result from the mid-twentieth century which requires surprisingly little background to prove. This note, suitable for undergraduates with experience of linear and abstract algebra, provides a complete and self-contained proof. All necessary pre-requisites, principally evaluation of homogeneous polynomials at projective points and Desargues' theorem are presented in full. While following the broad outline of Segre's proof, careful parameterisation of certain tangent lines results in shorter and simpler computations than the original. Comment: 13 pages, 2 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2301.05171 Zobrazit plný text záznamu View this record from Arxiv