Pure and Applied Mathematics Quarterly
Volume 12 (2016)
Special Issue: In Honor of Eduard Looijenga, Part 2 of 3
Guest Editor: Gerard van der Geer
Motivic vanishing cycles as a motivic measure
Pages: 33 – 74
We show that the motivic vanishing cycles introduced by J. Denef and F. Loeser give rise to a motivic measure on the Grothendieck ring of varieties over the affine line. We discuss the relation of this motivic measure to the motivic measure we constructed earlier using categories of matrix factorizations.
motivic vanishing cycles, motivic measure, Grothendieck ring of varieties, categorical measure, matrix factorizations, Thom–Sebastiani theorem