Rees Algebras of F-regular Type

AbstractWe study the F-regularity of Rees algebras R(I)=A[It] in terms of the global F-regularity of the blowing-up X=ProjR(I) of SpecA. 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,m) is a two-dimensional local ring and I is an m-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 X̃ on which IOX̃ is invertible. We also prove some miscellaneous results concerning singularities of Rees algebras and extended Rees algebras of higher dimension