$A_r$-stable curves and the Chow ring of $\overline{\mathcal{M}}_3$

Michele Pernice

$A_r$-stable curves and the Chow ring of $\overline{\mathcal{M}}_3$

Algebraic Geometry 2023-01-10 v2

Authors: Michele Pernice

Abstract

In this work, we introduce the moduli stack $\widetilde{\mathcal{M}}_{g,n}^r$ of $n$ -pointed, $A_r$ -stable curves of genus $g$ and use it to compute the Chow ring of $\overline{\mathcal{M}}_3$ . As a byproduct, we also compute the Chow ring of $\widetilde{\mathcal{M}}_3^7$ . All the Chow rings are assumed to be with coefficients in $\mathbb{Z}[1/6]$ .

Keywords

a_r-stable curves moduli stack chow ring moduli of curves genus three algebraic geometry

Cite

@article{arxiv.2211.09793,
  title  = {$A_r$-stable curves and the Chow ring of $\overline{\mathcal{M}}_3$},
  author = {Michele Pernice},
  journal= {arXiv preprint arXiv:2211.09793},
  year   = {2023}
}

Comments

This is the PhD thesis of the author; 129 pages; comments are very welcome

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