Asymptotic resurgence via integral closures
Asymptotic resurgence via integral closures
复制标题
通过积分闭包渐近复苏
DOI：
--
复制
发表时间：
2018
影响因子：
1.3
通讯作者：
Jay Schweig
中科院分区：
文献类型：
--
作者：
Michael DiPasquale;Christopher A. Francisco;Jeffrey Mermin;Jay Schweig
给定多项式环上的理想，我们证明了Guardo，Harbourne和Van Tuyl所研究的渐近再收敛可以用积分闭包来计算。因此，理想的渐近复苏性是涉及用Rees赋值定义的类Waldschmidt常数(我们称其为斜Waldschmidt常数)的有限多个比率的最大值。利用这一点，我们证明了如果理想是正规的(即，它的所有幂都是积分闭的)，则渐近再生性与再生性重合。
对于单项理想，斜Waldschmidt常数有一种解释，涉及Cooper、Embree、Ha和Hoefel定义的符号多面体。利用这种直觉，我们给出了几个无平方单项理想的例子，它们的复原性和渐近复原性是不同的。
Given an ideal in a polynomial ring, we show that the asymptotic resurgence studied by Guardo, Harbourne, and Van Tuyl can be computed using integral closures. As a consequence, the asymptotic resurgence of an ideal is the maximum of finitely many ratios involving Waldschmidt-like constants (which we call skew Waldschmidt constants) defined in terms of Rees valuations. We use this to prove that the asymptotic resurgence coincides with the resurgence if the ideal is normal (that is, all its powers are integrally closed).
For a monomial ideal the skew Waldschmidt constants have an interpretation involving the symbolic polyhedron defined by Cooper, Embree, Ha, and Hoefel. Using this intuition we provide several examples of squarefree monomial ideals whose resurgence and asymptotic resurgence are different.
无平方单项式理想的 Waldschmidt 常数
影响因子：
0.8
作者：
Bocci, Cristiano;Cooper, Susan;Guardo, Elena;Harbourne, Brian;Janssen, Mike;Nagel, Uwe;Seceleanu, Alexandra;Tuyl, Adam Van;Vu, Thanh
通讯作者：
Vu, Thanh