Sequences of Enumerative Geometry: Congruences and Asymptotics

Abstract

We study the integer sequence υ_n of numbers of lines in hypersurfaces of degree 2 _n − 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 υ _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.

Keywords:

• 11N37, 11N69, 11R45
• Sequence
• congruence
• asymptotic growth
• number of plane rational curves