Existence and unicity of pluriharmonic maps to Euclidean buildings and applications

2024/10/10 by Ya Deng, Deng, Ya, Chikako Mese +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2410.07871

openalex publication_date 2024/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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:π₁(X)→ 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.

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• Hyperbolicity and fundamental groups of complex quasi-projective varieties (II): via non-abelian Hodge theories

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