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October, 2021 Moduli space of quasimaps from $\mathbb{P}^{1}$ with two marked points to $\mathbb{P}(1,1,1,3)$ and $j$-invariant
Masao JINZENJI, Hayato SAITO
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J. Math. Soc. Japan 73(4): 995-1018 (October, 2021). DOI: 10.2969/jmsj/83148314

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 $-\log(j(\tau))$.

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Masao JINZENJI. Hayato SAITO. "Moduli space of quasimaps from $\mathbb{P}^{1}$ with two marked points to $\mathbb{P}(1,1,1,3)$ and $j$-invariant." J. Math. Soc. Japan 73 (4) 995 - 1018, October, 2021. https://doi.org/10.2969/jmsj/83148314

Information

Received: 14 August 2019; Revised: 25 March 2020; Published: October, 2021
First available in Project Euclid: 23 January 2021

Digital Object Identifier: 10.2969/jmsj/83148314

Subjects:
Primary: 14J33
Secondary: 14N35

Keywords: $j$-invariant , mirror symmetry , moduli space of quasimaps

Rights: Copyright ©2021 Mathematical Society of Japan

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Vol.73 • No. 4 • October, 2021
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