Exceptional loci of F-blowups and $G$-Hilbert schemes
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866915959168565248 |
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| author | Chávez-Martínez, Enrique Kaijima, Yutaro Yasuda, Takehiko |
| author_facet | Chávez-Martínez, Enrique Kaijima, Yutaro Yasuda, Takehiko |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_23591 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exceptional loci of F-blowups and $G$-Hilbert schemes Chávez-Martínez, Enrique Kaijima, Yutaro Yasuda, Takehiko Algebraic Geometry 14E15, 14B10, 14M25, 14L30 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. |
| title | Exceptional loci of F-blowups and $G$-Hilbert schemes |
| topic | Algebraic Geometry 14E15, 14B10, 14M25, 14L30 |
| url | https://arxiv.org/abs/2604.23591 |