Sequences of enumerative geometry: congruences and asymptotics
Abstract
We study the integer sequence vn of numbers of lines in hypersurfaces of degree 2n-3 of Pn, n>1. We prove a number of congruence properties of these numbers of several different types. Furthermore, the asymptotics of the vn 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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