Equivariant automorphisms of the Cox construction and applications
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917604458758144 |
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| author | Taroyan, Gregory |
| author_facet | Taroyan, Gregory |
| contents | In the present paper, we give a complete description of the group of holomorphic automorphisms of the Cox construction of a simplicial fan equivariant with respect to a large enough connected complex Lie subgroup of the large torus acting on the Cox construction. We then apply this description to find the groups of holomorphic automorphisms of rational moment-angle manifolds, including Calabi--Eckmann manifolds and Hopf manifolds. We also calculate the groups of equivariant automorphisms of complete simplicial toric varieties. This paper is the first in a series of two papers dedicated to studying the automorphism groups of toric stacks with applications to complex geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_02465 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant automorphisms of the Cox construction and applications Taroyan, Gregory Algebraic Geometry Algebraic Topology Complex Variables Symplectic Geometry 14M25, 32M18, 32L05, 32M05, 57S12, 14J50 In the present paper, we give a complete description of the group of holomorphic automorphisms of the Cox construction of a simplicial fan equivariant with respect to a large enough connected complex Lie subgroup of the large torus acting on the Cox construction. We then apply this description to find the groups of holomorphic automorphisms of rational moment-angle manifolds, including Calabi--Eckmann manifolds and Hopf manifolds. We also calculate the groups of equivariant automorphisms of complete simplicial toric varieties. This paper is the first in a series of two papers dedicated to studying the automorphism groups of toric stacks with applications to complex geometry. |
| title | Equivariant automorphisms of the Cox construction and applications |
| topic | Algebraic Geometry Algebraic Topology Complex Variables Symplectic Geometry 14M25, 32M18, 32L05, 32M05, 57S12, 14J50 |
| url | https://arxiv.org/abs/2403.02465 |