A319851 Welschinger invariant for the number of real plane curves of degree n passing through 3*n-1 general points.

1, 1, 8, 240, 18264, 2845440, 792731520, 359935488000, 248962406889600

Offset

1,3

Comments

a(n) is the Welschinger invariant #n.

Links

Table of n, a(n) for n=1..9.

Aubin Arroyo, Erwan Brugallé and Lucía López de Medrano, Recursive formulas for Welschinger invariants of the projective plane, International Mathematics Research Notices, 2011, 1107-1134; arXiv:0809.1541 [math.AG], 2008-2010. See numbers W2(n,0) in Section 7.3.

Erwan Brugallé, Géométries énumératives complexe, réelle et tropicale, Journées mathématiques X-UPS, École polytechnique, 2008. See Table 3, p. 54.

Antoine Chambert-Loir, Quand la géométrie devient tropicale, Pour la Science, No 492, October 2018 (in French).

I. Itenberg, V. Kharlamov & E. Shustin, Welschinger invariant and enumeration of real rational curves, Int. Math. Res. Not. (2003), no. 49, pp. 2639-2653.

I. Itenberg, V. Kharlamov & E. Shustin, Welschinger invariant and enumeration of real rational curves, arXiv:math/0303378 [math.AG], 2003.

I. Itenberg, V. Kharlamov & E. Shustin, Logarithmic equivalence of the Welschinger and the Gromov-Witten invariants, Uspekhi Mat. Nauk 59 (2004), no. 6(360), pp. 85-110.

I. Itenberg, V. Kharlamov & E. Shustin, Logarithmic equivalence of the Welschinger and the Gromov-Witten invariants, arXiv:math/0407188 [math.AG], 2004.

Crossrefs

Cf. A013587, A171118.

Sequence in context: A067360 A221770 A007060 * A320605 A302005 A301778

Adjacent sequences: A319848 A319849 A319850 * A319852 A319853 A319854

Keyword

nonn,more

Author

Georges Perrotte, Sep 29 2018

Extensions

a(8)-a(9) added from Arroyo et al. and name clarified by Andrey Zabolotskiy, May 03 2022, based on contribution by Michel Marcus

Status

approved