Geodesic
Welschinger invariants of small non-toric Del Pezzo surfaces
Journal of the European Mathematical Society, Tome 15 (2013) no. 2, pp. 539-594

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We give a recursive formula for purely real Welschinger invariants of the following real Del Pezzo surfaces: the projective plane blown up at q real and s≤1 pairs of conjugate imaginary points, where q+2s≤5, and the real quadric blown up at s≤1 pairs of conjugate imaginary points and having non-empty real part. The formula is similar to Vakil's recursive formula [22] for Gromov–Witten invariants of these surfaces and generalizes our recursive formula [12] for purely real Welschinger invariants of real toric Del Pezzo surfaces. As a consequence, we prove the positivity of the Welschinger invariants under consideration and their logarithmic asymptotic equivalence to genus zero Gromov–Witten invariants.
DOI : 10.4171/jems/367
Classification : 14-XX, 00-XX
Keywords: Tropical curves, real rational curves, enumerative geometry, Welschinger invariants, Caporaso–Harris formula 
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     author = {Ilia Itenberg and Viatcheslav Kharlamov and Eugenii Shustin},
     title = {Welschinger invariants of small non-toric {Del} {Pezzo} surfaces},
     journal = {Journal of the European Mathematical Society},
     pages = {539--594},
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Ilia Itenberg; Viatcheslav Kharlamov; Eugenii Shustin. Welschinger invariants of small non-toric Del Pezzo surfaces. Journal of the European Mathematical Society, Tome 15 (2013) no. 2, pp. 539-594. doi: 10.4171/jems/367

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