1996/02/14 by Luca Chiantini, Chiantini, Luca, Edoardo Sernesi +1
Mathematics · #Algebraic Geometry and Number Theory #Geometric Analysis and Curvature Flows #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.alg-geom/9602012
We study the family of irreducible curves with δ nodes belonging to a free linear system |C| with smooth general member on a surface S such that |KS| is ample. Under the assumption that C is numerically equivalent to pKS, p≥ 3 rational, we give an upper bound on δ ensuring that the family is smooth of codimension δ in |C| (plus another slightly different result of the same type). We give examples showing that the bound is sharp. Some related results concerning linear normality of nodal curves are proved.