Sequences of Enumerative Geometry: Congruences and Asymptotics, with an appendix by Don Zagier

Abstract

We study the integer sequence $v_n$ of numbers of lines in hypersurfaces of degree $2n-3$ of $\P^n$, $n>1$. We prove a number of congruence properties of these numbers of several different types. Furthermore, the asymptotics of the $v_n$ are described (in an appendix by Don Zagier). Finally, an attempt is made at carrying out a similar analysis for numbers of rational plane curves.