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arXiv · 2606.18253

Constant cycle surfaces on Fano varieties of cubic fourfolds

Jiexiang Huang
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Abstract

Huybrechts proved the finiteness of constant cycle curves of fixed order in any linear system $|L|$ on a K3 surface. In this paper, we study constant cycle surfaces on the Fano variety of lines $F(X)$ of a smooth cubic fourfold $X$. Fano surfaces $F(Y) \subset F(X)$ of hyperplane sections $Y \subset X$ are higher-dimensional analogues of curves on K3 surfaces. We prove that there are at most finitely many constant cycle surfaces of the form $F(Y)$ of any fixed order on $F(X)$.

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Jiexiang Huang. 2026-04-27. Constant cycle surfaces on Fano varieties of cubic fourfolds. https://arxiv.org/abs/2606.18253

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