Logarithmic equivalence of Welschinger and Gromov--Witten invariants
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 6, pp. 1093-1116
Voir la notice de l'article provenant de la source Math-Net.Ru
The Welschinger numbers, a kind of a real analogue of the Gromov–Witten numbers that count the complex rational curves through a given generic collection of points, bound from below the number of real rational curves for any generic collection of real points. Logarithmic equivalence of sequences is understood to mean the asymptotic equivalence of their logarithms.
Such an equivalence is proved for the Welschinger and Gromov–Witten numbers of any toric Del Pezzo surface with its tautological real structure, in particular, of the projective plane, under the hypothesis that all, or almost all, the chosen points are real. A study is also made of the positivity of Welschinger numbers and their monotonicity with respect to the number of
imaginary points.
@article{RM_2004_59_6_a5,
author = {I. V. Itenberg and V. M. Kharlamov and E. I. Shustin},
title = {Logarithmic equivalence of {Welschinger} and {Gromov--Witten} invariants},
journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
pages = {1093--1116},
publisher = {mathdoc},
volume = {59},
number = {6},
year = {2004},
language = {en},
url = {http://geodesic.mathdoc.fr/item/RM_2004_59_6_a5/}
}
TY - JOUR AU - I. V. Itenberg AU - V. M. Kharlamov AU - E. I. Shustin TI - Logarithmic equivalence of Welschinger and Gromov--Witten invariants JO - Trudy Matematicheskogo Instituta imeni V.A. Steklova PY - 2004 SP - 1093 EP - 1116 VL - 59 IS - 6 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/RM_2004_59_6_a5/ LA - en ID - RM_2004_59_6_a5 ER -
%0 Journal Article %A I. V. Itenberg %A V. M. Kharlamov %A E. I. Shustin %T Logarithmic equivalence of Welschinger and Gromov--Witten invariants %J Trudy Matematicheskogo Instituta imeni V.A. Steklova %D 2004 %P 1093-1116 %V 59 %N 6 %I mathdoc %U http://geodesic.mathdoc.fr/item/RM_2004_59_6_a5/ %G en %F RM_2004_59_6_a5
I. V. Itenberg; V. M. Kharlamov; E. I. Shustin. Logarithmic equivalence of Welschinger and Gromov--Witten invariants. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 59 (2004) no. 6, pp. 1093-1116. http://geodesic.mathdoc.fr/item/RM_2004_59_6_a5/