On the stratification of the discriminant varieties (Q1262414)

It is shown that the discriminant variety for the arrangements of type \(A_{\ell},B_{\ell}\) and \(D_{\ell}\) has canonical regular stratifications which are constructed in the standard way. Here the regularity means the b-regularity in the sense of Whitney. It is known that the b-regularity implies the a-regularity in the sense of Mather. For \(A_{\ell +1}\) and \(B_{\ell +1}\), we simply take \({\mathcal S}={\mathcal S}_{\min.}\), which is the minimal stratification. As the stratification \({\mathcal S}\) for \(D_{\ell +1}\), we take the restriction of \({\mathcal S}_{\min.}\) for \(B_{\ell +1}\) to \(D_{\ell +1}\).