arXiv subjects

Jiexiang Huang

Publications and source records attributed to Jiexiang Huang.

3 recordsLinked to original sources

arXiv2026

Constant cycle surfaces on Fano varieties of cubic fourfolds

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 $F(X)$.

math.AG↗

arXiv2025

Elliptic constant cycle curves on Kummer surfaces

The order of a constant cycle curve $C \subset X$ on a K3 surface, defined by Huybrechts, is a positive integer that measures the obstruction to decomposing the diagonal class $Δ_C$ in the Chow group $\mathrm{CH}^2(X \times C)$. In this paper, we compute the order of elliptic constant cycle curves that naturally arise on Kummer surfaces, by passing to the transcendental intermediate Jacobian $J_{\mathrm{tr}}^3(X \times C)$. As a consequence, every $n \in \mathbb{N}$ can be realized as the order of a constant cycle curve on a K3 surface.

math.AG↗

arXiv2023

The Curves of Elliptic Nodes on K3 Surfaces

Let $(X,L)$ be a polarized K3 surface of genus $g$ and $C_{en} \subset X$ be the curve of singular points of nodal elliptic curves in $|L|$. When $(X,L)$ is generic of genus two, Huybrechts observed that the curve $C_{en}$ is a constant cycle curve and conjectured that this remains true for higher genus cases. In this note, we show that the conjecture holds true for polarized K3 surfaces $(X,L)$ lying in a locus of codimension one in the moduli space of polarized K3 surfaces of genus $g$ for every $g > 2$.

math.AG↗