2019/01/31 by Takeo Nishinou, Nishinou, Takeo
Mathematics · Physics and Astronomy · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1901.11239
openalex publication_date 2019/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper studies the obstructions to deforming a map from a complex variety to another variety which is an immersion of codimension one. We extend the classical notion of semiregularity of subvarieties to maps between varieties, and show that it largely extends the applicability. Then we apply the main result to several situations. First, we give deformations of non-reduced curves on surfaces in a geometrically controlled way. Also, we give a simple but effective criterion for the vanishing of the obstructions to equisingular deformations of nodal curves on surfaces. Finally, we construct nodal curves with very small geometric genus on surfaces of general type.