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arXiv · 2604.23591

Exceptional loci of F-blowups and $G$-Hilbert schemes

Enrique Chávez-Martínez·Yutaro Kaijima·Takehiko Yasuda
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Abstract

We study exceptional loci of F-blowups of normal toric varieties. In the $\Q$-factorial case, this study amounts to studying the exceptional loci of $G$-Hilbert schemes. We give a formula for the dimension of the center of a prime divisor on the F-blowup in terms of combinatorial data, together with an algorithm for computing it. Moreover, we study the relation between F-blowups and essential divisors for three-dimensional terminal singularities and canonical singularities. Finally, we give a simple condition ensuring that a prime divisor over the given toric variety has a positive-dimensional center on the F-blowup.

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Enrique Chávez-Martínez, Yutaro Kaijima, Takehiko Yasuda. 2026-04-26. Exceptional loci of F-blowups and $G$-Hilbert schemes. https://arxiv.org/abs/2604.23591

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