arXiv subjects

Zaiyuan Chen

Publications and source records attributed to Zaiyuan Chen.

3 recordsLinked to original sources

arXiv2026

Bloch's conjecture for equivalences between twisted abelian surfaces and applications

The Beauville--Voisin conjecture predicts a canonical descending filtration on the Chow group of zero-cycles of a hyperkähler variety, opposite to the conjectural Bloch--Beilinson filtration. A basic test for such filtrations is a Bloch-type principle: the action on zero-cycles should be governed by the action on the holomorphic symplectic form. While this principle has been verified in several cases of hyperkähler varieties of $\mathrm{K3}^{[n]}$-type, the $\mathrm{Kum}_n$-type case remains much less understood. In this paper, we study this problem through twisted abelian surfaces and their associated $\mathrm{Kum}_n$-type varieties. We first construct a natural action of autoequivalences of twisted abelian surfaces on the Albanese kernel and prove Bloch's conjecture for all (anti-)symplectic autoequivalences. As an application, we prove the corresponding Bloch conjecture for symplectic birational automorphisms of twisted modular $\mathrm{Kum}_n$-type varieties; in particular, this applies to those admitting a birational Lagrangian fibration. Finally, we introduce and study a Shen--Yin--Zhao type filtration on twisted modular varieties and compare it with Voisin's filtration in the sixfold case. We also establish the anti-symplectic Bloch conjecture for twisted modular $\mathrm{Kum}_3$-type varieties.

math.AG↗

arXiv2026

TransXion: A High-Fidelity Graph Benchmark for Realistic Anti-Money Laundering

Money laundering poses severe risks to global financial systems, driving the widespread adoption of machine learning for transaction monitoring. However, progress remains stifled by the lack of realistic benchmarks. Existing transaction-graph datasets suffer from two pervasive limitations: (i) they provide sparse node-level semantics beyond anonymized identifiers, and (ii) they rely on template-driven anomaly injection, which biases benchmarks toward static structural motifs and yields overly optimistic assessments of model robustness. We propose TransXion, a benchmark ecosystem for Anti-Money Laundering (AML) research that integrates profile-aware simulation of normal activity with stochastic, non-template synthesis of illicit subgraphs.TransXion jointly models persistent entity profiles and conditional transaction behavior, enabling evaluation of "out-of-character" anomalies where observed activity contradicts an entity's socio-economic context. The resulting dataset comprises approximately 3 million transactions among 50,000 entities, each endowed with rich demographic and behavioral attributes. Empirical analyses show that TransXion reproduces key structural properties of payment networks, including heavy-tailed activity distributions and localized subgraph structure. Across a diverse array of detection models spanning multiple algorithmic paradigms, TransXion yields substantially lower detection performance than widely used benchmarks, demonstrating increased difficulty and realism. TransXion provides a more faithful testbed for developing context-aware and robust AML detection methods. The dataset and code are publicly available at https://github.com/chaos-max/TransXion.

cs.LG↗

arXiv2025

Filtrations on the derived category of twisted K3 surfaces

We introduce and study the Shen-Yin-Zhao filtration on derived categories of twisted K3 surfaces. A main contribution is the construction of a twisted Beauville-Voisin class $\mathfrak{o}_{\mathscr{X}} \in \operatorname{CH}_0(X)$ that extends fundamental results of O'Grady and Shen-Yin-Zhao \cite{OG13, SYZ20} to twisted settings. This class enables: 1. A derived equivalence-invariant filtration $\mathbf{S}_\bullet(\mathrm{D}^{(1)}(\mathscr{X}))$ preserved under Fourier-Mukai transforms, 2. A birational invariant filtration $\mathbf{S}^{\mathrm{SYZ}}_\bullet \operatorname{CH}_0$ on Bridgeland moduli spaces. We prove $\mathbf{S}^{\mathrm{SYZ}}_\bullet \operatorname{CH}_0$ coincides with Voisin's filtration $\mathbf{S}^{\mathrm{BV}}_\bullet\operatorname{CH}_0$ (Theorem 1.4), providing a canonical candidate for the conjectural Beauville-Voisin filtration. Applications include Bloch's conjecture for (anti)-symplectic automorphisms and existence of algebraically coisotropic subvarieties.

math.AG↗