On maximal generating degrees of powers of ideals
Speaker: Prof. Lê Tuấn Hoa

Time: 9:30 - 11:00, Wednesday December 01, 2021

Venue: Room 302, A5, Institute of Mathematics, VAST

Online: https://meet.google.com/esi-huxm-xqg

Abstract: The degree excess function $epsilon(I;n)$ is the difference between the maximal generating degree $d(I^n)$ of a homogeneous ideal $I$ of a polynomial ring and $p(I)n$, where $p(I)$ is the leading coefficient of the asymptotically linear function $d(I^n)$. It is shown that any non-increasing numerical function can be realized as a degree excess function, and there is a monomial ideal $I$ whose $epsilon(I;n)$ has exactly a given number of local maxima. In the case of monomial ideals, an upper bound on $epsilon(I;n)$ is provided. As an application it is shown that in the worst case, the so-called stability index of the Castelnuovo-Mumford regularity of a monomial ideal $I$ must be at least an exponential function of the number of variables.

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