# Welschinger invariants of small non-toric Del Pezzo surfaces

Ilia Itenberg; Viatcheslav Kharlamov; Eugenii Shustin

Journal of the European Mathematical Society (2013)

- Volume: 015, Issue: 2, page 539-594
- ISSN: 1435-9855

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topItenberg, 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 -

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