The Motivic Picard--Lefschetz Formula
Algebraic Geometry
2025-10-15 v1
Abstract
We prove a motivic enhancement of the classical Picard--Lefschetz formula. Our proof is completely motivic, and yields a description of the motivic nearby cycles at a quasi-homogeneous singularity, as well as its monodromy, in terms of an embedding of projective hypersurfaces.
Keywords
Cite
@article{arxiv.2510.12762,
title = {The Motivic Picard--Lefschetz Formula},
author = {Ran Azouri and Emil Jacobsen},
journal= {arXiv preprint arXiv:2510.12762},
year = {2025}
}
Comments
v1: Preliminary version. 30pp. Comments welcome!