TY - JOUR

T1 - Logarithmic equivalence of Welschinger and Gromov-Witten invariants

AU - Itenberg, I.

AU - Kharlamov, V.

AU - Shustin, E.

PY - 2004

Y1 - 2004

N2 - The Welschinger numbers, a kind of a real analogue of the GromovWitten 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.

AB - The Welschinger numbers, a kind of a real analogue of the GromovWitten 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.

UR - http://www.scopus.com/inward/record.url?scp=17744375988&partnerID=8YFLogxK

U2 - 10.1070/RM2004v059n06ABEH000797

DO - 10.1070/RM2004v059n06ABEH000797

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:17744375988

SN - 0036-0279

VL - 59

SP - 1093

EP - 1116

JO - Russian Mathematical Surveys

JF - Russian Mathematical Surveys

IS - 6

ER -