Resurgence and Waldschmidt constant of the ideal of a fat almost collinear subscheme in P2

Hassan Haghighi, Mohammad Mosakhani, Mohammad Zaman Fashami

Abstract


Let Zn=p0+p1+...+pn be a configuration of points in P2, where all points pi except p0 lie on a line, and let I(Zn) be its corresponding homogeneous ideal in K[P2]. The resurgence and the Waldschmidt constant of I(Zn) in [5] have been computed. In this note, we compute these two invariants for the defining ideal of a fat point subscheme Zn,c= cp0+p1+...+pn, i.e. the point p0 is considered with multiplicity c. Our strategy is similar to [5].

Keywords


fat points; containment problem; symbolic power; Waldschmidt constant; resurgence

Mathematics Subject Classification (2010)


Primary 13A15, 14N20; Secondary 13F20, 14N05

References


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