TY - JOUR

T1 - Welschinger invariants of toric Del Pezzo surfaces with nonstandard real structures

AU - Shustin, E.

N1 - Funding Information:
The research was supported by the grant no. 465/04 from the Israel Science Foundation, by the grant from the High Council for Scientific and Technological Cooperation between France and Israel at the Ministry of Science, Israel, and by the Hermann Minkowski Minerva Center for Geometry at the Tel Aviv University.

PY - 2007/9

Y1 - 2007/9

N2 - The Welschinger invariants of real rational algebraic surfaces are natural analogs of the Gromov-Witten invariants, and they estimate from below the number of real rational curves passing through prescribed configurations of points. We establish a tropical formula for the Welschinger invariants of four toric Del Pezzo surfaces equipped with a nonstandard real structure. Such a formula for real toric Del Pezzo surfaces with a standard real structure (i.e., naturally compatible with the toric structure) was established by Mikhalkin and the author. As a consequence we prove that for any real ample divisor D on a surface ∑ under consideration, through any generic configuration of c 1(∑)D - 1 generic real points, there passes a real rational curve belonging to the linear system |D|.

AB - The Welschinger invariants of real rational algebraic surfaces are natural analogs of the Gromov-Witten invariants, and they estimate from below the number of real rational curves passing through prescribed configurations of points. We establish a tropical formula for the Welschinger invariants of four toric Del Pezzo surfaces equipped with a nonstandard real structure. Such a formula for real toric Del Pezzo surfaces with a standard real structure (i.e., naturally compatible with the toric structure) was established by Mikhalkin and the author. As a consequence we prove that for any real ample divisor D on a surface ∑ under consideration, through any generic configuration of c 1(∑)D - 1 generic real points, there passes a real rational curve belonging to the linear system |D|.

UR - http://www.scopus.com/inward/record.url?scp=35148860792&partnerID=8YFLogxK

U2 - 10.1134/S0081543807030157

DO - 10.1134/S0081543807030157

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:35148860792

SN - 0081-5438

VL - 258

SP - 218

EP - 246

JO - Proceedings of the Steklov Institute of Mathematics

JF - Proceedings of the Steklov Institute of Mathematics

IS - 1

ER -