Title: Chow Rings of Mp_{0,2}(N,d) and Mbar_{0,2}(P^{N-1},d) and Gromov-Witten Invariants of Projective Hypersurfaces of Degree 1 and 2,
Abstract: In this paper, we prove formulas that represent two-pointed Gromov-Witten
invariant <O_{h^a}O_{h^b}>_{0,d} of projective hypersurfaces with d=1,2 in
terms of Chow ring of Mbar_{0,2}(P^{N-1},d), the moduli spaces of stable maps
from genus 0 stable curves to projective space P^{N-1}. Our formulas are based
on representation of the intersection number w(O_{h^a}O_{h^b})_{0,d}, which was
introduced by Jinzenji, in terms of Chow ring of Mp_{0,2}(N,d), the moduli
space of quasi maps from P^1 to P^{N-1} with two marked points. In order to
prove our formulas, we use the results on Chow ring of Mbar_{0,2}(P^{N-1},d),
that were derived by A. Mustata and M. Mustata. We also present explicit toric
data of Mp_{0,2}(N,d) and prove relations of Chow ring of Mp_{0,2}(N,d).