ncts

Let X be a complex algebraic variety. We explain how to produce a canonical compactification of its analytification X(C) by adding a Berkovich space at the boundary (the later being defined over the field C endowed with the trivial absolute value), building on earlier work by Morgan-Shalen, Berkovich, Favre, Thuillier, Fantini, Boucksom-Jonsson, etc. Our construction takes place in the setting of hybrid Berkovich spaces, which allows to get a compactification that is a locally ringed space and preserves several properties such as normality, regularity, etc. When the variety X is a moduli space of Riemann surfaces, we obtain a space related to Amini-Nicolussi’s hybrid compactification, which may be used to study the asymptotic behavior of families of Arakelov-Bergmann measures or Green functions. This last part is work in progress with Robert Wilms.