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arXiv · 2009.11634

Algebraic cycles and special Horikawa surfaces

Robert Laterveer
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Abstract

This note is about a $16$-dimensional family of surfaces of general type with $p_g=2$ and $q=0$ and $K^2=1$, called "special Horikawa surfaces". These surfaces, studied by Pearlstein-Zhang and by Garbagnati, are related to K3 surfaces. We show that special Horikawa surfaces have a multiplicative Chow-K\"unneth decomposition, in the sense of Shen-Vial. As a consequence, the Chow ring of special Horikawa surfaces displays K3-like behaviour.

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Robert Laterveer. 2020-09-24. Algebraic cycles and special Horikawa surfaces. https://arxiv.org/abs/2009.11634

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