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Title:
Finite subgroups of Cremona groups and representation dimension
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Abstract:
Cremona groups are infamously large. In particular, even the plane Cremona group cannot be embedded into a linear algebraic group. Their finite subgroups are much more manageable, but still not completely understood even in the rank 2 case over the complex numbers. However, lacking a complete classification, one may attempt to find bounds for their complexity. Over a number field, one can consider the orders of the finite subgroups. Over general fields, there is the Jordan constant. I consider the minimal dimension of a faithful representation. This is joint work with C. Urech.
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