**Seminario de Álgebra Conmutativa, Geometría Algebraica y Geometría Aritmética**

**Jueves 25 de febrero a las 10:30 h **

** Lugar: Teams (contactar con A. Bravo para la inclusión en el equipo) **

** Conferenciante: Christopher Heng Chiu (Universidad de Viena) **

** Título: Singularities of the arc space**

** Resumen: As the space of arcs of an algebraic variety is an infinite-dimensional scheme in all but the trivial cases, the study of its singularities is a difficult problem in general. One of the most important results in this direction is the theorem of Drinfeld, Grinberg and Kazhdan, which roughly says that the singular information of certain arcs is contained in a finite-dimensional model. In this talk we want to present a slightly different approach using a new formal invariant, which we call embedding codimension. This generalizes the notion of regularity defect as considered by Lech et. al. to the non-Noetherian case. We then prove a finiteness result for the arc space in terms of the embedding codimension and relate it to the Drinfeld model. Finally, we will give an outlook on how to approach a complete description of the singularities of the arc space. This is joint work with T. de Fernex and R. Docampo.**