A formula for the α-Futaki character
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914934573498368 |
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| author | Ghosh, Kartick |
| author_facet | Ghosh, Kartick |
| contents | Alvarez-Consul--Garcia-Fernandez--Garcia-Prada introduced the Kähler-Yang-Mills equations. They also introduced the $α$-Futaki character, an analog of the Futaki invariant, as an obstruction to the existence of the Kähler-Yang-Mills equations. The equations depend on a coupling constant $α$. Solutions of these equations with coupling constant $α>0$ are of utmost importance. In this paper, we provide a formula for the $α$-Futaki character on certain ample line bundles over toric manifolds. We then show that there are no solutions with $α>0$ on certain ample line bundles over certain toric manifolds and compute the value of $α$ if a solution exists. We also relate our result to the existence result of Keller-Friedman in dimension-two. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_01734 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A formula for the α-Futaki character Ghosh, Kartick Differential Geometry Alvarez-Consul--Garcia-Fernandez--Garcia-Prada introduced the Kähler-Yang-Mills equations. They also introduced the $α$-Futaki character, an analog of the Futaki invariant, as an obstruction to the existence of the Kähler-Yang-Mills equations. The equations depend on a coupling constant $α$. Solutions of these equations with coupling constant $α>0$ are of utmost importance. In this paper, we provide a formula for the $α$-Futaki character on certain ample line bundles over toric manifolds. We then show that there are no solutions with $α>0$ on certain ample line bundles over certain toric manifolds and compute the value of $α$ if a solution exists. We also relate our result to the existence result of Keller-Friedman in dimension-two. |
| title | A formula for the α-Futaki character |
| topic | Differential Geometry |
| url | https://arxiv.org/abs/2409.01734 |