2011/10/02 by Bin Wang, Wang, Bin
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #math.AG
paper · pdf · doi:10.48550/arxiv.1110.0185
openalex publication_date 2011/10/02 · arxiv created 2011/12/28 · arxiv updated 2011/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the continuation of our paper [10]. In this paper which is self contained, we would like to give a different obstruction formula to the FIRST order deformation of the pair of a smooth curve and a smooth hypersurface. This obstruction formula leads to a genus formula for a smooth curve in a smooth hypersurface. As an application we show that smooth elliptic curves in a smooth hypersurface of degree h≥ 2n-1 in the projective space \mathbf Pn, n≥ 3, can't deform in the first order to all hypersurfaces of the same degree. In particular, there are no smooth elliptic curves in generic hypersurfaces of degree h≥ 2n-1. This application in return leads to a study of the deformation of the pair mentioned above.