• Corpus ID: 238583537

The Chow rings of moduli spaces of elliptic surfaces over $\mathbb{P}^1$

@inproceedings{Canning2021TheCR,
  title={The Chow rings of moduli spaces of elliptic surfaces over \$\mathbb\{P\}^1\$},
  author={Samir Canning and Bochao Kong},
  year={2021}
}
Let EN denote the coarse moduli space of smooth elliptic surfaces over P 1 with fundamental invariant N . We compute the Chow ring A(EN ) for N ≥ 2. For each N ≥ 2, A(EN ) is Gorenstein with socle in codimension 16, which is surprising in light of the fact that the dimension of EN is 10N − 2. As an application, we show that the maximal dimension of a complete subvariety of EN is 16. When N = 2, the corresponding elliptic surfaces are K3 surfaces polarized by a hyperbolic lattice U . We show… 

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