Felix Klein's paper on real flexes vindicated
Volume 44 / 1998
Banach Center Publications 44 (1998), 195-210 DOI: 10.4064/-44-1-195-210
In a paper written in 1876 , Felix Klein gave a formula relating the number of real flexes of a generic real plane projective curve to the number of real bitangents at non-real points and the degree, which shows in particular that the number of real flexes cannot exceed one third of the total number of flexes. We show that Klein's arguments can be made rigorous using a little of the theory of singularities of maps, justifying in particular his resort to explicit examples.