On neighborhoods of embedded complex tori

2022/06/14 by Gong, Xianghong, Stolovitch, Laurent · 2 citations
#Algebraic Geometry (math.AG) #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2206.06842

Abstract

The goal of the article is to show that an n-dimensional complex torus embedded in a complex manifold of dimensional n+d, with a split tangent bundle, has neighborhood biholomorphic a neighborhood of the zero section in its normal bundle, provided the latter has (locally constant) Hermitian transition functions and satisfies a non-resonant Diophantine condition.

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• Pluripotential geometry on semi-positive effective divisors of numerical dimension one
• On neighborhoods of embedded toroidal and Hopf manifolds and their foliations

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