# University of Toronto's Symplectic Geometry Seminar

Sept. 27 2004, 12:10 - 1 ***NOTE DIFFERENT TIME ***

SS 2111 *** NOTE DIFFERENT ROOM ***

## Seongchun Kwon

###
Fields Institute

##
"Transversality properties on the moduli space of genus 0 stable maps
to a rational projective surface"

** Abstract: **
Transversality property is an intersection theoretic property. But
Tian related the non-transversality property to the singularity of the
stable map when the target space is a rational projective surface. I will
talk about ideas to calculate the pull-back cycles? intersection
multiplicities when the Gromov-Witten invariant is enumerative.
Surprisingly, intersection multiplicities are the same as the index of the
differentiation of the product of evaluation maps. I will also introduce
Tian?s establishment of the chamberwise real Gromov-Witten invariants and
explain the real enumerative implications of transversality properties. If
time allows, then I will explain how to calculate the full tangent space
splitting at any point on the moduli space in an intuitive way. This
calculation is a new generalization of the Konsevish?s normal bundle
splitting result. This talk is about the first result in the ongoing joint
project with Gang Tian.