INTRODUCTION to HILBERT SCHEMES EXERCISES Hilbert Form

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welcome to this new youtube channel dedicated to pedagogical explanations of research topics in mathematics for this first video i will give you an introduction to puncture hilbert schemes of the plane this talk is part of a master class given at the conference topics at the interface of low-dimensional group actions and geometric structures here we go [Music] the puncture headboard scheme is an interesting mathematical object because it allows different equivalent definitions which link together different areas of mathematics the most direct way to define it is to use algebraic geometry and to define it as a space of special ideals you can also define it in a geometric way as the blow up of the symmetric space finally you can also define it purely in terms of linear algebra as a space of pairs of commuting matrices the main part of this talk consists in describing these three viewpoints and to understand the links which exist between them to start consider endpoints of the plane the c