Motivic Integration on Toric Stacks
Alan Stapledon
TL;DR
This paper develops a combinatorial approach to motivic integration on toric stacks by decomposing the space of twisted arcs, enabling explicit calculations of integrals related to torus-invariant divisors.
Contribution
It introduces a novel decomposition of twisted arc spaces on toric stacks, facilitating combinatorial computation of motivic integrals.
Findings
Decomposition of twisted arc space for toric stacks
Explicit combinatorial description of motivic integrals
Application to torus-invariant divisors
Abstract
We present a decomposition of the space of twisted arcs of a toric stack. As a consequence, we give a combinatorial description of the motivic integral associated to a torus-invariant divisor of a toric stack.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Commutative Algebra and Its Applications · Algebraic Geometry and Number Theory