Welschinger invariants of small non-toric Del Pezzo surfaces

Itenberg, Ilia, Kharlamov, Viatcheslav, and Shustin, Eugenii. "Welschinger invariants of small non-toric Del Pezzo surfaces." Journal of the European Mathematical Society 015.2 (2013): 539-594. <http://eudml.org/doc/277407>.

@article{Itenberg2013,
abstract = {We give a recursive formula for purely real Welschinger invariants of the following real Del Pezzo surfaces: the projective plane blown up at$\sim q$ real and $s\le 1$ pairs of conjugate imaginary points, where $q+2s\le 5$, and the real quadric blown up at $s\le 1$ 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.},
author = {Itenberg, Ilia, Kharlamov, Viatcheslav, Shustin, Eugenii},
journal = {Journal of the European Mathematical Society},
keywords = {tropical curves; real rational curves; enumerative geometry; Welschinger invariants; Caporaso-Harris formula; tropical curves; real rational curves; enumerative geometry; Welschinger invariants; Caporaso-Harris formula},
language = {eng},
number = {2},
pages = {539-594},
publisher = {European Mathematical Society Publishing House},
title = {Welschinger invariants of small non-toric Del Pezzo surfaces},
url = {http://eudml.org/doc/277407},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Itenberg, Ilia
AU - Kharlamov, Viatcheslav
AU - Shustin, Eugenii
TI - Welschinger invariants of small non-toric Del Pezzo surfaces
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 2
SP - 539
EP - 594
AB - We give a recursive formula for purely real Welschinger invariants of the following real Del Pezzo surfaces: the projective plane blown up at$\sim q$ real and $s\le 1$ pairs of conjugate imaginary points, where $q+2s\le 5$, and the real quadric blown up at $s\le 1$ 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.
LA - eng
KW - tropical curves; real rational curves; enumerative geometry; Welschinger invariants; Caporaso-Harris formula; tropical curves; real rational curves; enumerative geometry; Welschinger invariants; Caporaso-Harris formula
UR - http://eudml.org/doc/277407
ER -