Singular loci of reflection arrangements and the containment problem

This paper provides insights into the role of symmetry in studying polynomial functions vanishing to high order on an algebraic variety. The varieties we study are singular loci hyperplane arrangements projective space, with emphasis arising from complex reflection groups. We provide minimal sets equations for radical ideals defining these and containments between ordinary symbolic powers ideals. Our work ties together generalizes results Bauer et al. (Int Math Res Not IMRN 24:7459–7514, 2019), Dumnicki (J Algebra 393:24–29, 2013), Harbourne Seceleanu Pure Appl 219(4):1062–1072, 2015) Malara Szpond 222(8):2323–2329, 2018) under a unified approach.