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arXiv · 2211.12059

Standard stable Horikawa surfaces

Julie Rana·Sönke Rollenske
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Abstract

We consider the stable compactification $\bar {\mathfrak H}$ of the moduli space of Horikawa surfaces with $K_X^2 = 2p_g(X) -4$. When $K_X^2 =8\ell$ we show that the closures of the two components $\mathfrak H^{\mathrm I}$ and $\mathfrak H^{\mathrm {II}}$ of the Gieseker moduli space intersect, for $\ell>2$ in a divisor parametrising explicitly described semi-smooth surfaces. With growing $K_X^2$ we find an increasing number of generically non-reduced irreducible components in the same connected component of the moduli space of stable surfaces.

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Julie Rana, Sönke Rollenske. 2022-11-22. Standard stable Horikawa surfaces. https://arxiv.org/abs/2211.12059

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