Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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The essential skeletons of pairs and the geometric P=W conjecture

Mirko Mauri

created by daniele on 25 Oct 2018

29 oct 2018 -- 15:30

Aula Mancini, SNS, Pisa

Abstract.

The geometric P=W conjecture is a conjectural description of the asymptotic behavior of the celebrated Nonabelian Hodge correspondence. In particular, it is expected that the dual boundary complex of the compactification of character varieties has the homotopy type of a sphere. In a joint work with Enrica Mazzon and Matthew Stevenson, we compute the first non-trivial examples of these dual boundary complexes in the compact case. This requires to develop a new theory of essential skeletons over a trivially-valued field. As a byproduct, inspired by these constructions, we show that certain character varieties appear in degenerations of compact hyper-Kähler manifolds. In this talk I will explain how these new non-archimedean techniques can shed new light into classical algebraic geometry problems.

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