Sequences of enumerative geometry: congruences and asymptotics, with an appendix by Don Zagier. (English) Zbl 1182.11047

The authors study the integer sequence \(v_n\) of numbers of lines in hypersurfaces of degree \(2n-3\) of \(\mathbb{P}^n\) for \(n>1\). They prove a number of congruence properties of these numbers of several different types. Also they derive some exact and some asymptotic formulas for the sequence \(v_n\). In addition, the authors present some results about numbers of rational curves in the plane.


11N69 Distribution of integers in special residue classes
11N37 Asymptotic results on arithmetic functions
11R45 Density theorems
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