Sequences of enumerative geometry: congruences and asymptotics

Details Sequences of enumerative geometry: congruences and asymptotics Sequences of enumerative geometry: congruences and asymptotics

2006-10-09

arxiv.org/abs/math/0610286v1

Mathematics

Number Theory

29 pages. Appendix by Don Zagier (pp. 24-28)

Scientific paper

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). An attempt is made at a similar analysis of two other enumerative sequences: the number of rational plane curves and the number of instantons in the quintic threefold.

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