Actions of diagonalizable $p$-groups and Chern numbers modulo $p$

Olivier Haution

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arXiv · 2412.02483

Actions of diagonalizable $p$-groups and Chern numbers modulo $p$

Olivier Haution

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Abstract

We obtain lower bounds for the dimension of fixed loci of diagonalizable $p$-groups acting on smooth projective varieties. Those bounds depend on the modulo $p$ Chern numbers of the ambient variety, and are expressed in a natural way by introducing an appropriate filtration on the "modulo $p$ cobordism ring" (for $p=2$ this is Thom's unoriented cobordism ring $MO^*$). They are obtained using equivariant localization methods, via the concentration theorem for the Chow ring, and by a technique of "partition dividing". As applications we derive statements in the spirit of Boardman's Five-Halves Theorem for involutions on manifolds.

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BibTeX RIS

Olivier Haution. 2024-12-03. Actions of diagonalizable $p$-groups and Chern numbers modulo $p$. https://arxiv.org/abs/2412.02483

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