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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 (1705.10048v2)

Published 29 May 2017 in math.AG

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_{ha}O_{hb})_{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 P1 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).

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