Equivariant $K$-theory of cellular toric varieties
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917909092106240 |
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| author | Uma, V. |
| author_facet | Uma, V. |
| contents | In this article we describe the $T_{comp}$-equivariant topological $K$-ring of a $T$-{\it cellular} complete toric variety. We further show that $K_{T_{comp}}^0(X)$ is isomorphic as an $R(T_{comp})$-algebra to the ring of piecewise Laurent polynomial functions on the associated fan denoted $PLP(Δ)$. Furthermore, we compute a basis for $K_{T_{comp}}^0(X)$ as a $R(T_{comp})$-module and multiplicative structure constants with respect to this basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_14201 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equivariant $K$-theory of cellular toric varieties Uma, V. K-Theory and Homology Algebraic Geometry Algebraic Topology 19L47, 14M25 In this article we describe the $T_{comp}$-equivariant topological $K$-ring of a $T$-{\it cellular} complete toric variety. We further show that $K_{T_{comp}}^0(X)$ is isomorphic as an $R(T_{comp})$-algebra to the ring of piecewise Laurent polynomial functions on the associated fan denoted $PLP(Δ)$. Furthermore, we compute a basis for $K_{T_{comp}}^0(X)$ as a $R(T_{comp})$-module and multiplicative structure constants with respect to this basis. |
| title | Equivariant $K$-theory of cellular toric varieties |
| topic | K-Theory and Homology Algebraic Geometry Algebraic Topology 19L47, 14M25 |
| url | https://arxiv.org/abs/2404.14201 |