Geodesic
New Cases of Logarithmic Equivalence of Welschinger and Gromov--Witten Invariants
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and singularities. Part 1, Tome 258 (2007), pp. 70-78

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We consider $\mathbb P^1\times\mathbb P^1$ equipped with the complex conjugation $(x,y)\mapsto(\bar y,\bar x)$ and blown up in at most two real or two complex conjugate points. For these four surfaces we prove the logarithmic equivalence of Welschinger and Gromov–Witten invariants. 
@article{TM_2007_258_a6,
     author = {I. V. Itenberg and V. M. Kharlamov and E. I. Shustin},
     title = {New {Cases} of {Logarithmic} {Equivalence} of {Welschinger} and {Gromov--Witten} {Invariants}},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {70--78},
     publisher = {mathdoc},
     volume = {258},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TM_2007_258_a6/}
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I. V. Itenberg; V. M. Kharlamov; E. I. Shustin. New Cases of Logarithmic Equivalence of Welschinger and Gromov--Witten Invariants. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Analysis and singularities. Part 1, Tome 258 (2007), pp. 70-78. http://geodesic.mathdoc.fr/item/TM_2007_258_a6/