On local holomorphic maps preserving invariant (p,p)-forms between bounded symmetric domains

2015/03/02 by Yuan Yuan, Yuan, Yuan · 1 citation
Mathematics · #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Geometry and complex manifolds #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1503.00585

openalex publication_date 2015/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let D, Ω₁, ..., Ω_m be irreducible bounded symmetric domains. We study local holomorphic maps from D into Ω₁ ×... Ω_m preserving the invariant (p, p)-forms induced from the normalized Bergman metrics up to conformal constants. We show that the local holomorphic maps extends to algebraic maps in the rank one case for any p and in the rank at least two case for certain sufficiently large p. The total geodesy thus follows if D=\mathbbBⁿ, Ω_i = \mathbbB^N_i for any p or if D=Ω₁ =...=Ω_m with rank(D)≥ 2 and p sufficiently large. As a consequence, the algebraic correspondence between quasi-projective varieties D / Γ preserving invariant (p, p)-forms is modular, where Γ is a torsion free, discrete, finite co-volume subgroup of Aut(D). This solves partially a problem raised by Mok.

Citations

• Submanifolds of Hermitian symmetric spaces

Cited by

• On local holomorphic maps between Hermitian manifolds preserving (p,p)-forms

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