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

2017/05/29 by Hayato Saito, Saito, Hayato
Computer Science · Mathematics · #14N35 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1705.10048

openalex publication_date 2017/05/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we prove formulas that represent two-pointed Gromov-Witten invariant _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^aO_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 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).

Citations

• Classical Computation of Number of Lines in Projective Hypersurfaces: Origin of Mirror Transformation

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