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
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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 -