2013/08/22 by Bauer, Thomas, Szemberg, Tomasz
#13C05 #14A05 #14C20 #14H20 #14N05 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1308.4983
There has been increased recent interest in understanding the relationship between the symbolic powers of an ideal and the geometric properties of the corresponding variety. While a number of results are available for the two-dimensional case, the higher-dimensional case is largely unexplored. In the present paper we study a natural conjecture arising from a result by Bocci and Chiantini. As a first step towards understanding the higher-dimensional picture, we show that this conjecture is true in dimension three. Also, we provide examples showing that the hypotheses of the conjecture may not be weakened.