663 research outputs found
Motivic zeta function via dlt modification
Given a smooth variety and a regular function on it, by considering
the dlt modification, we define the dlt motivic zeta function which does not depend on the choice of the dlt modification.Comment: 11 page
The essential skeleton of a degeneration of algebraic varieties
In this paper, we explore the connections between the Minimal Model Program
and the theory of Berkovich spaces. Let be a field of characteristic zero
and let be a smooth and proper -variety with semi-ample canonical
divisor. We prove that the essential skeleton of coincides with the
skeleton of any minimal -model and that it is a strong deformation retract
of the Berkovich analytification of . As an application, we show that the
essential skeleton of a Calabi-Yau variety over is a pseudo-manifold.Comment: To appear in American Journal of Mathematic
Poles of maximal order of motivic zeta functions
We prove a 1999 conjecture of Veys, which says that the opposite of the log
canonical threshold is the only possible pole of maximal order of Denef and
Loeser's motivic zeta function associated with a germ of a regular function on
a smooth variety over a field of characteristic zero. We apply similar methods
to study the weight function on the Berkovich skeleton associated with a
degeneration of Calabi-Yau varieties. Our results suggest that the weight
function induces a flow on the non-archimedean analytification of the
degeneration towards the Kontsevich-Soibelman skeleton.Comment: to appear in Duke Mathematical Journa
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