- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:05:09
Journal of the European Mathematical Society
J. Eur. Math. Soc.
JEMS
1435-9855
1435-9863
General
10.4171/JEMS
http://www.ems-ph.org/doi/10.4171/JEMS
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
15
2013
2
Welschinger invariants of small non-toric Del Pezzo surfaces
Ilia
Itenberg
Université de Strasbourg, STRASBOURG CEDEX, FRANCE
Viatcheslav
Kharlamov
Université de Strasbourg, STRASBOURG CEDEX, FRANCE
Eugenii
Shustin
Raymond and Beverly Sackler Faculty of Exact Scien, TEL AVIV, ISRAEL
Tropical curves, real rational curves, enumerative geometry, Welschinger invariants, Caporaso–Harris formula
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 $s \leq 1$ pairs of conjugate imaginary points, where $q+2s\le 5$, and the real quadric blown up at $s \leq 1$ pairs of conjugate imaginary points and having non-empty real part. The formula is similar to Vakil's recursive formula \cite{Va} for Gromov–Witten invariants of these surfaces and generalizes our recursive formula~\cite{IKS3} 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.
Algebraic geometry
General
539
594
10.4171/JEMS/367
http://www.ems-ph.org/doi/10.4171/JEMS/367