The Motivic Picard--Lefschetz Formula

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.

Publication Details

Journal
ArXiv.org
Published
2025-10-14
Primary Topic
Algebraic Geometry and Number Theory
Type
article
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article

The Motivic Picard--Lefschetz Formula

ArXiv.org
Algebraic Geometry and Number Theory
article

The Motivic Picard--Lefschetz Formula

article en

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.

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The Motivic Picard--Lefschetz Formula · ArXiv.org (2025) | TGRS Research Map | TGRS