The minimal free graded resolution of a star-configuration in PnPn

We find the minimal free graded resolution of the ideal of a star-configuration in PnPn of type (r,s)(r,s) defined by general forms in R=k[x0,x1,…,xn]R=k[x0,x1,…,xn]. This generalises the result of Ahn and Shin from a specific value of r=2r=2 to any value of 1≤r≤min⁡{n,s}1≤r≤min⁡{n,s}, and that of Geramita, Harbourne, and Migliore from a linear star-configuration in PnPn to a star-configuration in PnPn. Moreover, we show that any star-configuration in PnPn is arithmetically Cohen–Macaulay.