Time: 9h00, Wednesday, November 7, 2018
Location: Rom 611-612, Building A6, Institute of Mathematics

Abstract:Let $I$ be a monomial ideal in a polynomial ring over a field. Let $I^{(n)}$ be the $n$-th symbolic power of $I$. We prove that the regularity $\reg I^{(n)}$ and the maximal generating degree $d(I^{(n)})$ of $I^{(n)}$ are asymptotically quasi-linear functions of $n$ with a constant leading coefficient which are the same for both functions. For the cover ideal $J(G)$ of a graph $G$, we prove that $d(J(G)^{(n)})$ and $\reg (J(G)^{(n)})$ are quasi-linear of period $2$ for $n$ large.