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math.AG2025
The Drinfeld-Grinberg-Kazhdan theorem and embedding codimension of the arc space
Christopher Heng Chiu
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…
math.AG2023
On the formal neighborhood of a degenerate arc
Christopher Chiu, Herwig Hauser
We prove a result describing the structure of the formal neighborhoods of certain arcs in the arc space of an algebraic variety which are completely contained in the singular locus…
math.AG2021
Isosingular loci of algebraic varieties
Christopher Chiu, Herwig Hauser
We define the notion of isosingular loci of algebraic varieties, following the analytic case first studied by Ephraim. In particular, we give a partial extension of his main result…