Trung Nam Tran

Polynomial bounds for the stability of associated primes of monomial ideals

Let $I$ be a nonzero proper monomial ideal in ${\rm k}[x_1,\ldots,x_r]$, and let $d$ be the maximal degree of a minimal monomial generator. We prove that the index of stability of the associated primes of its ordinary powers satisfies \[ {\rm astab}(I)\le\frac{(4e)^{r-1}}4\,d^{r-1}\qquad(r\ge3), \] while ${\rm astab}(I...