Title: Motivic generating series for toric surface singularities
Authors: Nicaise, Johannes # ×
Issue Date: May-2005
Publisher: Cambridge univ press
Series Title: Mathematical proceedings of the cambridge philosophical society vol:138 pages:383-400
Abstract: Lejeune-Jalabert and Reguera computed the geometric Poincare series P_{geom}(T) for toric surface singularities. They raised the question whether this series equals the arithmetic Poincare series. We prove this equality for a class of toric varieties including the surfaces, and construct a counterexample in the general case. We also compute the motivic Igusa Poincaré series Q_{geom}(T) for toric surface singularities, using the change of variables formula for motivic integrals, thus answering a second question of Lejeune-Jalabert and Reguera's. The series Q_{geom}(T) contains more information than the geometric series, since it determines the dimension of the tangent space at the singularity. In some sense, this is the only difference between Q_{geom}(T) and P_{geom}(T).
ISSN: 0305-0041
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
× corresponding author
# (joint) last author

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