On the tacnodes of configurations of conics in the projective plane (Q1923276)

The authors consider arrangements of \(k\) conics in a projective plane having nodes and tacnodes as only singularities. They prove that if the characteristic of the base field is not two, then the number of tacnodes has an upper bound of the form \(Ck^e\) where \(C>0\) and \(e<2\). This gives a negative answer to a question raised by \textit{F. Hirzebruch} [in: ``Algebraic Geometry'', Proc. Lefschetz Centen. Conf., Mexico City 1984, Part I, Contemp. Math. 58, 141-155 (1986; Zbl 0601.14030)]. The proof uses results from graph theory.