Counting rational curves with multiple points and Gromov-Witten invariants of blow-ups

Details Counting rational curves with multiple points and Gromov-Witten invariants of blow-ups Counting rational curves with multiple points and Gromov-Witten invariants of blow-ups

1996-09-14

arxiv.org/abs/alg-geom/9609010v1

Mathematics

Algebraic Geometry

24 pages

Scientific paper

We study Gromov-Witten invariants on the blow-up of P^n at a point, which is probably the simplest example of a variety whose moduli spaces of stable maps do not have the expected dimension. It is shown that many of these invariants can be interpreted geometrically on P^n as certain numbers of rational curves having a multiple point of given order at the blown up point. Moreover, all these invariants can actually be calculated, giving enumerative invariants of P^n which have not been known before.

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