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arXiv · 1912.10387

A two-dimensional family of surfaces of general type with $p_g=0$ and $K^2=7$

Yifan Chen·YongJoo Shin
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Abstract

We study the construction of complex minimal smooth surfaces $S$ of general type with $p_g(S)=0$ and $K_S^2=7$. Inoue constructed the first examples of such surfaces, which can be described as Galois $\mathbb{Z}_2\times\mathbb{Z}_2$-covers over the four-nodal cubic surface. Later the first named author constructed more examples as Galois $\mathbb{Z}_2\times\mathbb{Z}_2$-covers over certain six-nodal del Pezzo surfaces of degree one. In this paper we construct a two-dimensional family of minimal smooth surfaces of general type with $p_g=0$ and $K^2=7$, as Galois $\mathbb{Z}_2\times\mathbb{Z}_2$-covers of certain rational surfaces with Picard number three, with eight nodes and with two elliptic fibrations. This family is different from the previous ones.

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Yifan Chen, YongJoo Shin. 2019-12-22. A two-dimensional family of surfaces of general type with $p_g=0$ and $K^2=7$. https://arxiv.org/abs/1912.10387

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