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|.
|Number of pages||29|
|Journal||Proceedings of the Steklov Institute of Mathematics|
|State||Published - Sep 2007|