Complete toric varieties with semisimple automorphism group
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908795271118848 |
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| author | Galland, Gabriel Barría |
| author_facet | Galland, Gabriel Barría |
| contents | Let $X$ be a complete toric variety. We give a criterion to decide whether $X$ decomposes as a product of complete toric varieties by analyzing the $1$-skeleton of its fan. More precisely, we prove that any direct-sum decomposition of the 1-skeleton induces a corresponding direct-sum decomposition of the fan itself. As an application, we show that if the identity component of the automorphism group is semisimple, then $X$ must be a product of projective spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20375 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Complete toric varieties with semisimple automorphism group Galland, Gabriel Barría Algebraic Geometry 14M25, 14J50 Let $X$ be a complete toric variety. We give a criterion to decide whether $X$ decomposes as a product of complete toric varieties by analyzing the $1$-skeleton of its fan. More precisely, we prove that any direct-sum decomposition of the 1-skeleton induces a corresponding direct-sum decomposition of the fan itself. As an application, we show that if the identity component of the automorphism group is semisimple, then $X$ must be a product of projective spaces. |
| title | Complete toric varieties with semisimple automorphism group |
| topic | Algebraic Geometry 14M25, 14J50 |
| url | https://arxiv.org/abs/2511.20375 |