| Abstract: The binomial sum formula of symbolic powers, adjoint of two ideals, has been extensively studied. This has both geometric and combinatorial significance. So, our goal in this talk is to address the following questions: 1. For which classes of ideals $I$ in a polynomial ring $R_1$ and $J$ in a polynomial ring $R_2$, the binomial sum formula of rational powers of the ideal $I+J$ in the fiber product ring of $R_1$ and $R_2$ hold? 2. Is there a relationship between Rees valuations of $I$ in the ring $R_1$, Rees valuations of $J$ in the ring $R_2$, and Rees valuations of $I+J$ in the fiber product ring of $R_1$ and $R_2$? To address questions 1 and 2, we work with standard monomials and introduce a new class of ideals called ideals with the 'Rees Package'.
This is a joint work with Sankhaneel Bisui, Huy Tai Ha, and Jonathan Montano. |