Welschinger invariants of toric Del Pezzo surfaces with non-standard real structures

Details Welschinger invariants of toric Del Pezzo surfaces with non-standard real structures Welschinger invariants of toric Del Pezzo surfaces with non-standard real structures

2006-05-27

arxiv.org/abs/math/0605697v1

Mathematics

Algebraic Geometry

An extended version of MPI Preprint no. MPIM2005-44

Scientific paper

The Welschinger invariants of real rational algebraic surfaces are natural analogues 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 non-standard 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 surfaces $\Sigma$ under consideration, through any generic configuration of $c_1(\Sigma)D-1$ generic real points there passes a real rational curve belonging to the linear system $|D|$.

Affiliated with

Also associated with

No associations

Rating

Welschinger invariants of toric Del Pezzo surfaces with non-standard real structures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Welschinger invariants of toric Del Pezzo surfaces with non-standard real structures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Welschinger invariants of toric Del Pezzo surfaces with non-standard real structures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-680786