2019/06/19 by Tohaneanu, Stefan, Xie, Yu · 1 citation
#Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.1906.08346
Let Σ be a finite collection of linear forms in \mathbb K[x0,…,xn], where \mathbb K is a field. Denote \rm Supp(Σ) to be the set of all nonproportional elements of Σ, and suppose \rm Supp(Σ) is generic, meaning that any n+1 of its elements are linearly independent. Let 1≤ a≤ |Σ|. In this article we prove the conjecture that the ideal generated by (all) a-fold products of linear forms of Σ has linear graded free resolution. As a consequence we prove the Geramita-Harbourne-Migliore conjecture concerning the primary decomposition of ordinary powers of defining ideals of star configurations, and we also determine the resurgence of these ideals.