arXiv subjects

Christopher Heng Chiu

Publications and source records attributed to Christopher Heng Chiu.

2 recordsLinked to original sources

arXiv2026

The Drinfeld-Grinberg-Kazhdan theorem and embedding codimension of the arc space

We prove an extension of the theorem of Drinfeld, Grinberg and Kazhdan to arcs with arbitrary residue field. As an application we show that the embedding codimension is generically constant on each irreducible subset of the arc space which is not contained in the singular locus. In the case of maximal divisorial sets, this relates the corresponding finite formal models with invariants of singularities of the underlying variety. We also prove an extension of a theorem by Bourqui and Sebag characterizing arcs of embedding codimension 0.

math.AG↗

arXiv2026

The singular locus of a GL-variety

A $\mathbf{GL}$-variety is a (typically) infinite dimensional variety $X$ equipped with an action of the infinite general linear group. In recent work of the first two authors with Draisma, a candidate definition for the singular locus of $X$ was put forth. The approach there made use of auxiliary finite dimensional varieties associated to $X$. In this paper, we give a number of characterizations of the singular locus that are intrinsic to $X$. This work shows that the candidate definition is clearly correct, and helps clarify the geometric meaning of singular points.

math.AG↗