Sequences of enumerative geometry: congruences and asymptotics
Number Theory
2012-07-30 v1 Algebraic Geometry
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). 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.
Keywords
Cite
@article{arxiv.math/0610286,
title = {Sequences of enumerative geometry: congruences and asymptotics},
author = {Daniel B. Grunberg and Pieter Moree},
journal= {arXiv preprint arXiv:math/0610286},
year = {2012}
}
Comments
29 pages. Appendix by Don Zagier (pp. 24-28)