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Some Algebro-Geometric Aspects of the Fourth Painlevé Equation

Enrico Schlitzer
Institution: 
SISSA
Location: 
A-134
Schedule: 
Thursday, February 8, 2018 - 11:00 to 12:00
Abstract: 

In this seminar, starting from the symmetric form of PIV, I will characterize the group of Backlund transformations and I will describe its action on the solutions of PIV. Then I will consider PIV as an Hamiltonian system, introducing the notion of tau function. I will derive the set of differential equations satisfied by the tau functions and the associated action of the Backlund transformation group. Finally I will describe the space of initial values of PIV, obtained by eight blow-ups of P1 \times P1, showing that the surface-type is E_6^1; in this framework, the Backlund transformation group is understood as acting on certain divisors on the surface.

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