arXiv subjects

Ken Sato

Publications and source records attributed to Ken Sato.

9 recordsLinked to original sources

arXiv2026

Higher Chow cycles, cyclic cubic fourfolds and Lagrangian subvarieties

In this paper we initiate the study of higher Chow cycles on holomorphic symplectic manifolds. Our concrete central result is construction of explicit indecomposable (2,1)- and (4,1)-cycles on the Fano varieties of lines on cyclic cubic fourfolds. This is the first explicit example of such cycles on holomorphic symplectic manifolds. The proof of indecomposability is done by degeneration to cuspidal cubic fourfolds. Along the way, we develop a method of inducing (p,1)-cycles on Hilbert squares of K3 surfaces. Finally, we study restriction of (2,1)-cycles to Lagrangian subvarieties, and observe the phenomenon that the restricted cycles are always decomposable in the examples in our hand.

math.AG↗

arXiv2026

Construction of higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$, Part II

In this paper, we construct higher Chow cycles of type $(2, 1)$ on a family of surfaces related to a product of curves, which are certain degree $N$ abelian covers of $\mathbb{P}^1$ branched over $n+2$ points. We prove that for a very general member, these cycles generate a subgroup of the indecomposable part of $\operatorname{rank} \ge n\cdot \varphi(N)$, where $\varphi(N)$ is Euler's totient function, by computing their images under the transcendental regulator map.

math.AG↗

arXiv2025

Notes on symplectic action on $(2,1)$-cycles on $K3$ surfaces

In this paper, we propose and study a conjecture that symplectic automorphisms of a $K3$ surface $X$ act trivially on the indecomposable part $\mathrm{CH}^2(X,1)_{\mathrm{ind}}\otimes \mathbb{Q}$ of Bloch's higher Chow group. This is a higher Chow analogue of Huybrechts' conjecture on the symplectic action on $0$-cycles. We give several partial results verifying our conjecture, some conditional and some unconditional. Our unconditional results include the full proof for Kummer surfaces of product type.

math.AG↗

arXiv2025

Construction of Higher Chow cycles on cyclic coverings of $\mathbb{P}^1 \times \mathbb{P}^1$

In this paper, we construct higher Chow cycles of type $(2, 1)$ on a certain family of surfaces, which are constructed by a product of certain hypergeometric curves of degree $N$. We prove that for a very general member, these cycles are linearly independent over $\mathbb{Z}$ and generate a subgroup of $\operatorname{rank} \ge 36 \cdot \varphi(N)$, where $\varphi(N)$ is Euler's totient function, by computing the image of the transcendental regulator map.

math.AG↗

arXiv2025

Higher Chow cycles on Eisenstein K3 surfaces

We construct higher Chow cycles of type (2,1) on some families of K3 surfaces with non-symplectic automorphisms of order 3 and prove that our cycles are indecomposable for very general members. The proof is a combination of some degeneration arguments, and explicit computations of the regulator map.

math.AG↗

arXiv2024

Higher Chow cycles on K3 surfaces attached to plane quartics

In this paper, we give an explicit construction of higher Chow cycles of type $(2,1)$ on $K3$ surfaces obtained as quadruple coverings of the projective plane ramified along smooth quartics. The construction uses a pair of bitangents of the quartics. We prove that the higher Chow cycles generate a rank 2 subgroup in the indecomposable part of the higher Chow group for very general members, by using a specialization argument and an explicit computation of the regulator map.

math.AG↗

arXiv2023

Higher Chow cycles on some K3 surfaces with involution

We construct, for each 2<r<18, an explicit family of higher Chow cycles of type (2,1) on a family of lattice-polarized K3 surfaces of generic Picard rank r, and prove that the indecomposable part of this cycle is non-torsion for very general members of the family. These are the first explicit examples of such families in middle Picard rank. Our construction is based on singular double plane model of K3 surfaces, and the proof of indecomposability is done by a degeneration method.

math.AG↗

arXiv2022

Higher Chow cycles on a family of Kummer surfaces

We construct a collection of families of higher Chow cycles of type $(2,1)$ on a 2-dimensional family of Kummer surfaces, and prove that for a very general member, they generate a subgroup of rank $\ge 18$ in the indecomposable part of the higher Chow group. Construction of the cycles uses a finite group action on the family, and the proof of their linear independence uses Picard-Fuchs differential operators.

math.AG↗

arXiv2016

Fabry-Pérot interference in a triple-gated quantum point contact

We demonstrated that a triple-gated GaAs quantum point contact, which has an additional surface gate between a pair of split gates to strengthen the lateral confinement, produces the well-defined quantized conductance and Fabry-Pérot-type (FP-type) oscillations on it even using a relatively low mobility wafer. A one-dimensional phenomenological model potential was developed to explain the oscillatory behavior. By combining the model calculations and dc bias spectroscopy, we obtained detailed information about the energy scales of the oscillatory structures. The relationships between the FP-type oscillations and the anomaly below the first plateau will be addressed.

cond-mat.mes-hall↗