2010/06/24 by Jack Huizenga, Huizenga, Jack
Mathematics · #14H50 #14J28 #14J29 #14J70 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H50 #msc:14J28 #msc:14J29 #msc:14J70
paper · pdf · doi:10.48550/arxiv.1006.4686
21 pages, 1 figure. Version 3 streamlines the exposition considerably
arxiv created 2011/01/04 · arxiv updated 2011/01/06
Given a surface S in P3 and a collection of general points on it, how many surfaces of a given degree intersect S in a curve with prescribed multiplicities at the points? We formulate two natural conjectures which would answer this question, and we show they are equivalent. We then prove these conjectures in case all multiplicities are small.