Moduli space of quasimaps from ℙ¹ with two marked points to 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 ℙ¹ with two marked points to weighted projective space 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(𝜏)).