The geometry of Frobenius on toric varieties
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908391652196352 |
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| author | Carvajal-Rojas, Javier Özavcı, Emre Alp |
| author_facet | Carvajal-Rojas, Javier Özavcı, Emre Alp |
| contents | We give a geometric description of the positivity of the Frobenius-trace kernel on a $\mathbb{Q}$-factorial projective toric variety. To do so, we define its Frobenius support as well as the notions of $F$-effectiveness for divisors and $1$-cycles. As it turns out, the interaction of the corresponding cone of $F$-effective curves with the Mori cone of curves reflects the type of extremal Mori contractions that the variety can undergo. As a corollary, we obtain that the Frobenius-trace kernel is ample if and only if the Picard rank is $1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02994 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The geometry of Frobenius on toric varieties Carvajal-Rojas, Javier Özavcı, Emre Alp Algebraic Geometry 14G17, 14M25, 14E30, 14J45, 14M17 We give a geometric description of the positivity of the Frobenius-trace kernel on a $\mathbb{Q}$-factorial projective toric variety. To do so, we define its Frobenius support as well as the notions of $F$-effectiveness for divisors and $1$-cycles. As it turns out, the interaction of the corresponding cone of $F$-effective curves with the Mori cone of curves reflects the type of extremal Mori contractions that the variety can undergo. As a corollary, we obtain that the Frobenius-trace kernel is ample if and only if the Picard rank is $1$. |
| title | The geometry of Frobenius on toric varieties |
| topic | Algebraic Geometry 14G17, 14M25, 14E30, 14J45, 14M17 |
| url | https://arxiv.org/abs/2506.02994 |