Formal Neighbourhoods and Formal Models of Non-Degenerate Arcs

Authors

  • Peter Petrov Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

DOI:

https://doi.org/10.7546/CRABS.2022.12.01

Keywords:

non-degenerate arc, formal neighbourhood, formal model, embedding codimension

Abstract

An important result about the geometry of the arc space of an algebraic variety is the theorem of Drinfeld–Grinberg–Kazhdan, representing the formal neighbourhood of a non-degenerate arc. We start with a brief review of some important results and notions. Then the complete proof of the theorem with examples is given. A generalization to the relative case is discussed for smooth and ´etale morphisms.

Author Biography

Peter Petrov, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences

Mailing Address:
Institute of Mathematics and Informatics,
Bulgarian Academy of Sciences
Akad. G. Bonchev St, Bl. 8,
1113 Sofia, Bulgaria

E-mail: pk5rov@gmail.com

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Published

23-12-2022

How to Cite

[1]
P. Petrov, “Formal Neighbourhoods and Formal Models of Non-Degenerate Arcs”, C. R. Acad. Bulg. Sci., vol. 75, no. 12, pp. 1707–1714, Dec. 2022.

Issue

Section

Mathematics