In this paper we present various particular versions of the general patchworking procedure for the construction of reduced algebraic curves with prescribed singularities on algebraic surfaces. Among the main examples are a deformation of reducible algebraic curves on reducible algebraic surfaces in the presence of non-transverse intersections of a curve with the singular locus of a surface, and a deformation of curves with multiple components. As an application we deduce a significant asymptotical improvement for the sufficient existence criterion of algebraic curves with arbitrary prescribed singularities in given linear systems on smooth projective algebraic surfaces.
ASJC Scopus subject areas
- Mathematics (all)