Existence and unicity of pluriharmonic maps to Euclidean buildings and applications
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866915147556061184 |
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| author | Deng, Ya Mese, Chikako |
| author_facet | Deng, Ya Mese, Chikako |
| contents | Given a complex smooth quasi-projective variety $X$, a reductive algebraic group $G$ defined over some non-archimedean local field $K$ and a Zariski dense representation $\varrho:π_1(X)\to G(K)$, we construct a $\varrho$-equivariant pluriharmonic map from the universal cover of $X$ into the Bruhat-Tits building $Δ(G)$ of $G$, with appropriate asymptotic behavior. We also establish the uniqueness of such a pluriharmonic map in a suitable sense, and provide a geometric characterization of these equivariant maps. This paper builds upon and extends previous work by the authors jointly with G. Daskalopoulos and D. Brotbek. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07871 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Existence and unicity of pluriharmonic maps to Euclidean buildings and applications Deng, Ya Mese, Chikako Complex Variables Algebraic Geometry Differential Geometry Given a complex smooth quasi-projective variety $X$, a reductive algebraic group $G$ defined over some non-archimedean local field $K$ and a Zariski dense representation $\varrho:π_1(X)\to G(K)$, we construct a $\varrho$-equivariant pluriharmonic map from the universal cover of $X$ into the Bruhat-Tits building $Δ(G)$ of $G$, with appropriate asymptotic behavior. We also establish the uniqueness of such a pluriharmonic map in a suitable sense, and provide a geometric characterization of these equivariant maps. This paper builds upon and extends previous work by the authors jointly with G. Daskalopoulos and D. Brotbek. |
| title | Existence and unicity of pluriharmonic maps to Euclidean buildings and applications |
| topic | Complex Variables Algebraic Geometry Differential Geometry |
| url | https://arxiv.org/abs/2410.07871 |