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Wall-crossing integral Chow rings of $\overline{\mathcal M}_{1,n}$

Luca Battistella, Andrea Di Lorenzo

Abstract

We compute the integral Chow rings of $\overline{\mathcal M}_{1,n}$ for $n=3,4$. For $n\leq 6$, these stacks can be obtained by a sequence of weighted blow-ups and blow-downs from a simple stack, either a weighted projective space or a Grassmannian. Our strategy consists in inductively computing all the integral Chow rings of the alternative compactifications introduced by Smyth and studied by Lekili-Polishchuk.

Wall-crossing integral Chow rings of $\overline{\mathcal M}_{1,n}$

Abstract

We compute the integral Chow rings of for . For , these stacks can be obtained by a sequence of weighted blow-ups and blow-downs from a simple stack, either a weighted projective space or a Grassmannian. Our strategy consists in inductively computing all the integral Chow rings of the alternative compactifications introduced by Smyth and studied by Lekili-Polishchuk.
Paper Structure (2 sections, 2 theorems, 3 equations)

This paper contains 2 sections, 2 theorems, 3 equations.

Table of Contents

  1. Introduction

Key Result

Theorem 1

Let $\overline{\mathcal{M}}_{1,3}$ be the moduli stack of stable $3$-pointed curves of genus one over a field of characteristic $0$. The integral Chow ring admits the following presentation: where the generators are $\lambda$ (the first Chern class of the Hodge line bundle), and the classes of four boundary divisors $\delta_{\emptyset}, \delta_1,\delta_2,\delta_3$, where the index represents the

Theorems & Definitions (2)

  • Theorem
  • Theorem