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).
Finally, an attempt is made at carrying out a similar analysis for numbers of
rational plane curves.
Publié le : 2008-05-15
Classification:
Sequence,
congruence,
asymptotic growth,
number of plane rational curves,
11N37,
11N69,
11R45
@article{1243429954,
author = {Gr\"unberg, Daniel B. and Moree, Pieter},
title = {Sequences of Enumerative Geometry: Congruences and Asymptotics, with an appendix by Don Zagier},
journal = {Experiment. Math.},
volume = {17},
number = {1},
year = {2008},
pages = { 409-426},
language = {en},
url = {http://dml.mathdoc.fr/item/1243429954}
}
Grünberg, Daniel B.; Moree, Pieter. Sequences of Enumerative Geometry: Congruences and Asymptotics, with an appendix by Don Zagier. Experiment. Math., Tome 17 (2008) no. 1, pp. 409-426. http://gdmltest.u-ga.fr/item/1243429954/