Characterization on projective submanifolds of codimensions 2 and 3

2020/07/19 by Ping Li, Li, Ping, Fangyang Zheng +1
Mathematics · #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Algebraic Geometry and Number Theory

paper · pdf · doi:10.48550/arxiv.2007.09678

Abstract

In this article we give a necessary and sufficient condition to characterize projective submanifolds in \mathbb P^N with codimensions 2 and 3. The conditions involve the Chern classes of the manifold and a very ample line bundle on the manifold. This generalizes our earlier characterization for hypersurfaces. The higher codimensional cases are proposed as a general question.

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