On Connections Between Invariants of Singularities in Zero and Positive Characteristics.

[摘要] In the first part we study the partition given by the regions where the mixed test ideals are constant. We show that each region can be described as a p-fractal. In addition, we give some examples illustrating that these regions do not need to be composed of finitely many rational polytopes. In the second part we introduce two families of ideals, F-jumping ideals and F-Jacobian ideals, in order to study the singularities of hypersurfaces in positive characteristic. In addition, we use F-Jacobian ideals to study intrinsic properties of the singularities of hypersurfaces. In particular, we give conditions for F-regularity. Moreover, we prove several properties of F-Jacobian ideals that resemble those of Jacobian ideals of polynomials.

[发布机构] University of Michigan

[效力级别] F-Jumping numbers

[关键词] Constancy Regions;F-Jumping numbers;F-Jacobian;Mathematics;Science;Mathematics