Genus g Gromov-Witten invariants of Del Pezzo surfaces: Counting plane curves with fixed multiple points

Details Genus g Gromov-Witten invariants of Del Pezzo surfaces: Counting plane curves with fixed multiple points Genus g Gromov-Witten invariants of Del Pezzo surfaces: Counting plane curves with fixed multiple points

1997-09-04

arxiv.org/abs/alg-geom/9709004v1

Mathematics

Algebraic Geometry

LaTeX2e

Scientific paper

As another application of the degeneration methods of [V3], we count the number of irreducible degree $d$ geometric genus $g$ plane curves, with fixed multiple points on a conic $E$, not containing $E$, through an appropriate number of general points in the plane. As a special case, we count the number of irreducible genus $g$ curves in any divisor class $D$ on the blow-up of the plane at up to five points (no three collinear). We then show that these numbers give the genus $g$ Gromov-Witten invariants of the surface. Finally, we suggest a direction from which the remaining del Pezzo surfaces can be approached, and give a conjectural algorithm to compute the genus g Gromov-Witten invariants of the cubic surface.

Affiliated with

Also associated with

No associations

Rating

Genus g Gromov-Witten invariants of Del Pezzo surfaces: Counting plane curves with fixed multiple points 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 Genus g Gromov-Witten invariants of Del Pezzo surfaces: Counting plane curves with fixed multiple points, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Genus g Gromov-Witten invariants of Del Pezzo surfaces: Counting plane curves with fixed multiple points will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-328355