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SUMMARY:An Introduction to the Geometry of Jet Schemes and Arc Spaces
DTSTART:20220707T090000
DTEND:20220707T100000
DTSTAMP:20260916T032124Z
UID:950d5d75fd10158dd8515e3c95511f85b1e1a30ee903a7067552f8a7
CATEGORIES:Conferences - Seminars
DESCRIPTION:Ilaria Rossinelli\, École Polytechnique Fédérale de Lausann
 e\nJet schemes and arc spaces over a variety were introduced by Nash\, who
  was probably the first to notice that geometric properties of arcs are re
 lated to ones of the variety. Moreover\, they were also discovered to pla
 y a fundamental role in the theory of motivic integration started by Konts
 evich\, which in turn offers powerful tools to work on them and obtain eve
 n more properties and results. \n\nThis expository talk will be divided i
 nto two main parts. We will start defining jet schemes and arc spaces of v
 arieties (eventually in characteristic zero)\, and discuss their construct
 ion as representations of certain functors. Then\, we will move onto the s
 tudy of their geometric properties\, focusing in particular on how these p
 rovide geometric information and insight about the variety.\n\nIf time per
 mits\, we will also briefly discuss how jets and arcs are used in motivic 
 integration\, and how this powerful machinery leads to even more informati
 on.
LOCATION:MA B1 524 https://plan.epfl.ch/?room==MA%20B1%20524
STATUS:CONFIRMED
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