1999/11/23 by Alberto Calabri, Calabri, Alberto, Rita Ferraro +1
Mathematics · #14J17 #32S25 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14J17 #msc:32S25
paper · pdf · doi:10.48550/arxiv.math/9911183
31 pages; partially rewritten
arxiv created 2002/03/13 · arxiv updated 2009/11/30
Locally analytically, any isolated double point occurs as a double covering of a smooth surface. It can be desingularized via the canonical resolution, as it is well-known. In this paper we explicitly compute the fundamental cycle of both the canonical and minimal resolution of a double point singularity and we classify those for which the fundamental cycle differs from the fiber cycle. Finally we compute the conditions that a double point imposes to pluricanonical systems.