RC-POSITIVITY, VANISHING THEOREMS AND RIGIDITY OF HOLOMORPHIC MAPS

2018/07/31 by Xiaokui Yang
Mathematics · #Analyticity of holomorphic functions #Complex manifold #Cotangent bundle #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Hermitian manifold #Holomorphic function #Homotopy and Cohomology in Algebraic Topology #Identity theorem #Line bundle #Normal bundle #Tangent bundle #math.AG #math.CV #math.DG #msc:14F17 #msc:32L20 #msc:53C55

paper · pdf · doi:10.1017/s1474748019000471

published as J. Inst. Math. Jussieu 20 (2021) 1023-1038

openalex created_date 2018/07/19 · arxiv created 2018/09/04 · openalex publication_date 2019/10/11 · arxiv updated 2021/07/01 · openalex updated_date 2026/08/05

Abstract

Abstract Let M and N be two compact complex manifolds. We show that if the tautological line bundle O_T_M^∗ (1) is not pseudo-effective and O_T_N^∗ (1) is nef, then there is no non-constant holomorphic map from M to N . In particular, we prove that any holomorphic map from a compact complex manifold M with RC-positive tangent bundle to a compact complex manifold N with nef cotangent bundle must be a constant map. As an application, we obtain that there is no non-constant holomorphic map from a compact Hermitian manifold with positive holomorphic sectional curvature to a Hermitian manifold with non-positive holomorphic bisectional curvature.

Citations

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