2015/05/04 by Zhenjian Wang, Wang, Zhenjian
Mathematics · Physics and Astronomy · #14J70 #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic and Geometric Analysis #FOS: Mathematics #Geometric Analysis and Curvature Flows #Primary 14A25 #Secondary 14C34
paper · pdf · doi:10.48550/arxiv.1505.00615
openalex publication_date 2015/05/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Jacobian ideal provides the set of infinitesimally trivial deformations for a homogeneous polynomial, or for the corresponding complex projective hypersurface. In this article, we investigate whether the associated linear deformation is indeed trivial, and show that the answer is no in a general situation. We also give a characterization of tangentially smoothable hypersurfaces with isolated singularities. Our results have applications in the local study of variations of projective hypersurfaces, complementing the global versions given by J. Carlson and P. Griffiths, R. Donagi and the author, and in the study of isotrivial linear systems on the projective space, showing that a general divisor does not belong to an isotrivial linear system of positive dimension.