Resurgence and Waldschmidt constant of the ideal of a fat almost collinear subscheme in P 2

摘要

Let Z n =p 0 +p 1 +...+p n be a configuration of points in P 2 , where all points p i except p 0 lie on a line, and let I ( Z n ) be its corresponding homogeneous ideal in K [ P 2 ]. The resurgence and the Waldschmidt constant of I ( Z n ) in [5] have been computed. In this note, we compute these two invariants for the defining ideal of a fat point subscheme Z n,c = cp 0 +p 1 +...+p n , i.e. the point p 0 is considered with multiplicity c. Our strategy is similar to [5].