Research of ring-invariants associated to powers of ideals

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We give a calculation method of the diagonal F-thresholds on binomial hypersurfaces. Moreover, we prove an inequality on the diagonal F-thresholds, the a-invariant (due to Goto and Watanabe) and the F-pure thresholds on standard graded affine toric rings. We discuss Cohen-Macaulay properties of powers of edge ideals of simple graphs, and characterize graphs higher powers of edge ideals for which are Cohen-Macaulay. Furthermore, we give a similar result in the case of second power. As an application of Skoda's theorem, we prove a variant of Wang's theorem (about Goto number).