A319851 - OEIS

%I #19 May 03 2022 10:45:03

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

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

%C a(n) is the Welschinger invariant #n.

%H Aubin Arroyo, Erwan Brugallé and Lucía López de Medrano, <a href="https://doi.org/10.1093/imrn/rnq096">Recursive formulas for Welschinger invariants of the projective plane</a>, International Mathematics Research Notices, 2011, 1107-1134; arXiv:<a href="https://arxiv.org/abs/0809.1541">0809.1541</a> [math.AG], 2008-2010. See numbers W2(n,0) in Section 7.3.

%H Erwan Brugallé, <a href="http://www.math.polytechnique.fr/xups/xups08-02.pdf">Géométries énumératives complexe, réelle et tropicale</a>, Journées mathématiques X-UPS, École polytechnique, 2008. See Table 3, p. 54.

%H Antoine Chambert-Loir, <a href="https://www.pourlascience.fr/sd/mathematiques/quand-la-geometrie-devient-tropicale-14757.php">Quand la géométrie devient tropicale</a>, Pour la Science, No 492, October 2018 (in French).

%H I. Itenberg, V. Kharlamov & E. Shustin, <a href="https://doi.org/10.1155/S1073792803131352">Welschinger invariant and enumeration of real rational curves</a>, Int. Math. Res. Not. (2003), no. 49, pp. 2639-2653.

%H I. Itenberg, V. Kharlamov & E. Shustin, <a href="https://arxiv.org/abs/math/0303378">Welschinger invariant and enumeration of real rational curves</a>, arXiv:math/0303378 [math.AG], 2003.

%H I. Itenberg, V. Kharlamov & E. Shustin, <a href="https://doi.org/10.4213/rm797">Logarithmic equivalence of the Welschinger and the Gromov-Witten invariants</a>, Uspekhi Mat. Nauk 59 (2004), no. 6(360), pp. 85-110.

%H I. Itenberg, V. Kharlamov & E. Shustin, <a href="https://arxiv.org/abs/math/0407188">Logarithmic equivalence of the Welschinger and the Gromov-Witten invariants</a>, arXiv:math/0407188 [math.AG], 2004.

%Y Cf. A013587, A171118.

%K nonn,more

%O 1,3

%A _Georges Perrotte_, Sep 29 2018

%E a(8)-a(9) added from Arroyo et al. and name clarified by _Andrey Zabolotskiy_, May 03 2022, based on contribution by _Michel Marcus_