Rees Algebras of F-regular Type,

We study the F-regularity of Rees algebras R(I) = A[It] in terms of the global F-regularity of the blowing-up X = Proj R(I) of Spec A. As it reads, global F-regularity is a global analog of strong F-regularity defined via splitting of Frobenius maps in prime characteristic, and these notions are extended to characteristic zero by reduction modulo p 0. We study in detail the case where (A, ) is a two-dimensional local ring and I is an -primary ideal. In characteristic zero, the condition for R(I) to have F-regular type is described in terms of the dual graph of a resolution on which I is invertible. We also prove some miscellaneous results concerning singularities of Rees algebras and extended Rees algebras of higher dimension