ID 62802
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Author
Puthenpurakal, Tony J.
Abstract
Let K be a field and consider the standard grading on A = K[X1, ... ,Xd]. Let I, J be monomial ideals in A. Let In(J) = (In : J) be the nth symbolic power of I with respect to J. It is easy to see that the function fI J (n) = e0(In(J)/In) is of quasi-polynomial type, say of period g and degree c. For n ≫ 0 say

fIJ (n) = ac(n)nc + ac−1(n)nc−1 + lower terms,

where for i = 0, ... , c, ai : N → Q are periodic functions of period g and ac ≠0. In [4, 2.4] we (together with Herzog and Verma) proved that dim In(J)/In is constant for n ≫ 0 and ac(−) is a constant. In this paper we prove that if I is generated by some elements of the same degree and height I ≥ 2 then ac−1(−) is also a constant.
Keywords
quasi-polynomials
monomial ideals
symbolic powers
Note
Mathematics Subject Classification. Primary 13D40; Secondary 13H15.
Published Date
2022-01
Publication Title
Mathematical Journal of Okayama University
Volume
volume64
Issue
issue1
Publisher
Department of Mathematics, Faculty of Science, Okayama University
Start Page
187
End Page
190
ISSN
0030-1566
NCID
AA00723502
Content Type
Journal Article
language
英語
Copyright Holders
Copyright ©2022 by the Editorial Board of Mathematical Journal of Okayama University
File Version
publisher
Refereed
True
Submission Path
mjou/vol64/iss1/11