Multiplier ideals and integral closure of monomial ideals: An analytic approach
Authors:Jeffery D. McNeal and Yunus E. Zeytuncu Journal:
Proc. Amer. Math. Soc. 140 (2012), 1483-1493
MSC (2010):
Primary 13P99, 14Q99, 32S45; Secondary 14M25, 13B22
Posted:
August 22, 2011
Full-text PDF
Abstract: Proofs of two results about a monomial ideal - describing membership in auxiliary ideals associated to the monomial ideal - are given which do not invoke resolution of singularities. The AM-GM inequality is used as a substitute for taking a log resolution of the monomial ideal.
6.David
Eisenbud, Commutative algebra, Graduate Texts in Mathematics,
vol. 150, Springer-Verlag, New York, 1995. With a view toward
algebraic geometry. MR 1322960
(97a:13001)
7.Heisuke
Hironaka, Resolution of singularities of an algebraic variety over
a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964),
109–203; ibid. (2) 79 (1964), 205–326. MR 0199184
(33 #7333)
9.Robert
Lazarsfeld, Positivity in algebraic geometry. II, Ergebnisse
der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys
in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A
Series of Modern Surveys in Mathematics], vol. 49, Springer-Verlag,
Berlin, 2004. Positivity for vector bundles, and multiplier ideals. MR 2095472
(2005k:14001b)
13.Yum
Tong Siu, An effective Matsusaka big theorem, Ann. Inst.
Fourier (Grenoble) 43 (1993), no. 5, 1387–1405
(English, with English and French summaries). MR 1275204
(95f:32035)
16.Yum-Tong
Siu, Extension of twisted pluricanonical sections with
plurisubharmonic weight and invariance of semipositively twisted
plurigenera for manifolds not necessarily of general type, Complex
geometry (Göttingen, 2000) Springer, Berlin, 2002,
pp. 223–277. MR 1922108
(2003j:32027a)
17.Bernard
Teissier, Variétés polaires. II. Multiplicités
polaires, sections planes, et conditions de Whitney, Algebraic
geometry (La Rábida, 1981) Lecture Notes in Math., vol. 961,
Springer, Berlin, 1982, pp. 314–491 (French). MR 708342
(85i:32019)