scholarly journals Motivic integration on the Hitchin fibration

2021 ◽  
pp. 196-230
Author(s):  
François Loeser ◽  
Dimitri Wyss
Keyword(s):  
Motivic Integration ◽  
Hitchin Fibration

Motivic Integration in Josquin's "Motets"

1977 ◽  
Vol 21 (2) ◽  
pp. 264 ◽  
Author(s):  
Irving Godt ◽  
Josquin
Keyword(s):  
Motivic Integration

Motivic Integration

2018 ◽  
Author(s):  
Antoine Chambert-Loir ◽  
Johannes Nicaise ◽  
Julien Sebag
Keyword(s):  
Motivic Integration

scholarly journals Tropical refined curve counting via motivic integration

2018 ◽  
Vol 22 (6) ◽  
pp. 3175-3234 ◽  
Author(s):  
Johannes Nicaise ◽  
Sam Payne ◽  
Franziska Schroeter
Keyword(s):  
Motivic Integration

scholarly journals POINCARÉ SERIES FOR SEVERAL PLANE DIVISORIAL VALUATIONS

2003 ◽  
Vol 46 (2) ◽  
pp. 501-509 ◽  
Author(s):  
F. Delgado ◽  
S. M. Gusein-Zade
Keyword(s):  
Plane Curve ◽  
Poincaré Series ◽  
Finite Collection ◽  
Curve Singularity ◽  
Motivic Integration ◽  
Poincare Series ◽  
Plane Curve Singularity ◽  
Functions Of Two Variables ◽  
Irreducible Components ◽  
Divisorial Valuations

AbstractWe compute the (generalized) Poincaré series of the multi-index filtration defined by a finite collection of divisorial valuations on the ring $\mathcal{O}_{\mathbb{C}^2,0}$ of germs of functions of two variables. We use the method initially elaborated by the authors and Campillo for computing the similar Poincaré series for the valuations defined by the irreducible components of a plane curve singularity. The method is essentially based on the notions of the so-called extended semigroup and of the integral with respect to the Euler characteristic over the projectivization of the space of germs of functions of two variables. The last notion is similar to (and inspired by) the notion of the motivic integration.AMS 2000 Mathematics subject classification: Primary 14B05; 16W70

scholarly journals The motivic Thom–Sebastiani theorem for regular and formal functions

2018 ◽  
Vol 2018 (735) ◽  
pp. 175-198 ◽  
Author(s):  
Quy Thuong Lê
Keyword(s):  
Analogous Result ◽  
Motivic Integration ◽  
Crucial Element ◽  
Regular Functions ◽  
Formal Schemes ◽  
Theoretic Proof

AbstractThanks to the work of Hrushovski and Loeser on motivic Milnor fibers, we give a model-theoretic proof for the motivic Thom–Sebastiani theorem in the case of regular functions. Moreover, slightly extending Hrushovski–Loeser’s construction adjusted to Sebag, Loeser and Nicaise’s motivic integration for formal schemes and rigid varieties, we formulate and prove an analogous result for formal functions. The latter is meaningful as it has been a crucial element of constructing Kontsevich–Soibelman’s theory of motivic Donaldson–Thomas invariants.

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