2020/05/11 by Brian Harbourne, Harbourne, Brian, Jake Kettinger +3
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Polynomial and algebraic computation #Algebraic Geometry and Number Theory
paper · pdf · doi:10.48550/arxiv.2005.05282
We show that two ostensibly different versions of the asymptotic resurgence\nintroduced by Guardo, Harbourne and Van Tuyl in 2013 are the same. We also show\nthat the resurgence and asymptotic resurgence attain their maximal values\nsimultaneously, if at all, which we apply to a conjecture of Grifo. For radical\nideals of points, we show that the resurgence and asymptotic resurgence attain\ntheir minimal values simultaneously. In addition, we introduce an integral\nclosure version of the resurgence and relate it to the other versions of the\nresurgence. In closing we provide various examples and raise some related\nquestions, and we finish with some remarks about computing the resurgence.\n