arXiv subjects

Tai-Hsuan Chung

Publications and source records attributed to Tai-Hsuan Chung.

2 recordsLinked to original sources

arXiv2026

Semi-abelian reduction of Albanese varieties

Let X_K be a projective geometrically normal variety over the fraction field of a DVR. We show that if X_K admits a projective model whose special fibre has at worst nodes in codimension one, then the Albanese variety Alb_{X_K/K} has semi-abelian reduction over the same base. As an application, we extend the classical nonexistence theorem of Fontaine and Abrashkin for abelian schemes over Z to the singular setting. For instance, if a flat projective Z-scheme X has normal and geometrically connected fibres, then H^1(X_Q, O_{X_Q})=0.

math.AG↗

arXiv2024

Stable Reduction via the Log Canonical Model

We formulate a stable reduction conjecture that extends Deligne-Mumford's stable reduction to higher dimensions and provide a simple proof that it holds in large characteristic, assuming two standard conjectures of the Minimal Model Program. As a result, we recover the Hacon-Kovács theorem on the properness of the moduli stack $\overline{\mathscr{M}}_{2,v,k}$ of stable surfaces of volume $v$ defined over $k=\overline{k}$, provided that $\operatorname{char}k>C(v)$, a constant depending only on $v$.

math.AG↗