Elliptic constant cycle curves on Kummer surfaces

2025/06/06 by Huang, Jiexiang
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.06260

Abstract

The order of a constant cycle curve C ⊂ 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 CH²(X × 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_tr³(X × C). As a consequence, every n ∈ ℕ can be realized as the order of a constant cycle curve on a K3 surface.

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