Moduli space of quasimaps from $\mathbb{P}^{1}$ with two marked points to $\mathbb{P}(1,1,1,3)$ and $j$-invariant

Abstract

In this paper, we construct toric data of moduli space of quasimaps of degree $d$ from $\mathbb{P}^{1}$ with two marked points to weighted projective space $\mathbb{P}(1,1,1,3)$. With this result, we prove that the moduli space is a compact toric orbifold. We also determine its Chow ring. Moreover, we give a proof of the conjecture proposed by Jinzenji that a series of intersection numbers of the moduli spaces coincides with expansion coefficients of inverse function of $-\log(j(\tau))$.