Motives of Certain Hyperplane Sections of Milnor Hypersurfaces

Evan Marth

Motives of Certain Hyperplane Sections of Milnor Hypersurfaces

Algebraic Geometry 2025-07-10 v2

Authors: Evan Marth

Abstract

We construct a hyperplane section $Y$ of a Milnor hypersurface associated to a regular semisimple endomorphism $\varphi$ . Exploiting its structure as a hyperplane section of a projective bundle and its natural torus action, we give a motivic decomposition of $Y$ , which encodes both the cellular structure of $Y$ and the arithmetic of the eigenvalues of $\varphi$ . This decomposition is proven without using the "nilpotence principle", that is to say there are no "phantoms".

Keywords

motives Milnor hypersurface hyperplane section projective bundle torus action cellular decomposition regular semisimple endomorphism

Cite

@article{arxiv.2507.05434,
  title  = {Motives of Certain Hyperplane Sections of Milnor Hypersurfaces},
  author = {Evan Marth},
  journal= {arXiv preprint arXiv:2507.05434},
  year   = {2025}
}

Comments

7 pages. Corrected misprint in statement of Theorem 1.1

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