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ABSTRACT
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Let ( R , m ) \\left ( {R,m} \\right ) be a complete local domain containing the rationals. If I ⊆ R I \\subseteq R is a one-fibered ideal then there is a constant l l , depending only on R R and I I , such that if f ∈ m f \\in m and f ∉... more
Let ( R , m ) \\left ( {R,m} \\right ) be a complete local domain containing the rationals. If I ⊆ R I \\subseteq R is a one-fibered ideal then there is a constant l l , depending only on R R and I I , such that if f ∈ m f \\in m and f ∉ I n f \\notin {I^n} , then there exists a derivation d d such that d ( f ) ∉ I n + l d\\left ( f \\right ) \\notin {I^{n + l}} .
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This paper gives new bounds on the first Hilbert coefficient of an ideal of finite colength in a Cohen-Macaulay local ring. The bound given is quadratic in the multiplicity of the ideal. We compare our bound to previously known bounds and... more
This paper gives new bounds on the first Hilbert coefficient of an ideal of finite colength in a Cohen-Macaulay local ring. The bound given is quadratic in the multiplicity of the ideal. We compare our bound to previously known bounds and give examples to show that at least in some cases it is sharp. The techniques come largely from work of Elias, Rossi, Valla, and Vasconcelos.
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88 Craig Huneke, Tight closure and its applications. 1996 87 John Erik Forneess, Dynamics in several complex variables, 1996 86 Sorin Popa, Classification of subfactors and their endomorphisms, 1995 85 Michlo Jimbo and Tetsuji Miwa, ...
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Abstract: This article is based on five lectures the author gave during the summer school, Interactions between Homotopy Theory and Algebra, from July 26August 6, 2004, held at the University of Chicago, organized by Lucho Avramov, Dan... more
Abstract: This article is based on five lectures the author gave during the summer school, Interactions between Homotopy Theory and Algebra, from July 26August 6, 2004, held at the University of Chicago, organized by Lucho Avramov, Dan Christensen, Bill Dwyer, ...
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In this paper we give new lower bounds on the Hilbert-Kunz multiplicity of unmixed nonregular local rings, bounding them uniformly away from 1. Our results improve previous work of Aberbach and Enescu.
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ABSTRACT Without Abstract
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This article was occasioned by a three-week program in commutative algebra held at the Mathematical Sciences Research Institute (MSRI) in Berkeley from June 15-July 2, 1987. Those who have not been to the Institute have been deprived of a... more
This article was occasioned by a three-week program in commutative algebra held at the Mathematical Sciences Research Institute (MSRI) in Berkeley from June 15-July 2, 1987. Those who have not been to the Institute have been deprived of a spectacular view of the ...
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For certain classes of rings we give an affirmative answer to whether there exists a uniform bound on the least power of the tight closure of an arbitrary ideal which lies in the ideal. The rings need to have the property that modulo each... more
For certain classes of rings we give an affirmative answer to whether there exists a uniform bound on the least power of the tight closure of an arbitrary ideal which lies in the ideal. The rings need to have the property that modulo each minimal prime there exists a resolution ...
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We study a notion called n-standardness (defined by M.E. Rossi (2000) in [10] and extended in this paper) of ideals primary to the maximal ideal in a Cohen–Macaulay local ring and some of its consequences. We further study conditions... more
We study a notion called n-standardness (defined by M.E. Rossi (2000) in [10] and extended in this paper) of ideals primary to the maximal ideal in a Cohen–Macaulay local ring and some of its consequences. We further study conditions under which the maximal ideal is 3-standard, first proving results for when the residue field has prime characteristic and then using the method of reduction to prime characteristic to extend the results to the equicharacteristic 0 case. As an application, we extend a result due to T. Puthenpurakal (2005) [9] and show that a certain length associated with a minimal reduction of the maximal ideal does not depend on the minimal reduction chosen.
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ABSTRACT Motivated by a question of Stillman, we find a sharp upper bound for the projective dimension of ideals of height two generated by quadrics. In a polynomial ring with arbitrary large number of variables, we prove that ideals... more
ABSTRACT Motivated by a question of Stillman, we find a sharp upper bound for the projective dimension of ideals of height two generated by quadrics. In a polynomial ring with arbitrary large number of variables, we prove that ideals generated by n quadrics define cyclic modules with projective dimension at most 2n - 2. We refine this bound according to the multiplicity of the ideal. We ask whether tight upper bounds for the projective dimension of ideals generated by quadrics can be expressed only in terms of their height and number of minimal generators.
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Page 1. TIGHT CLOSURE AND THE KODAIRA VANISHING THEOREM Craig Huneke and Karen E. Smith 1. Introduction In its familiar form, the Kodaira Vanishing Theorem is a statement about the cohomology of ...
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0. Introduction. Let R be a local ring, and I an ideal of R. Associated to I are several graded algebras: the symmetric algebra of the module I, Sym (I), the Rees algebra of I, defined to be the algebra R (I)=(Gn= O InF, and the... more
0. Introduction. Let R be a local ring, and I an ideal of R. Associated to I are several graded algebras: the symmetric algebra of the module I, Sym (I), the Rees algebra of I, defined to be the algebra R (I)=(Gn= O InF, and the associated graded algebra of I, gr1 (R)= RII Gii/2 (?.. ...
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... J. 28 (1981) 199-222 [PS] Peskine, G, Szpiro, L.: Dimension projective finie et cohomologie locale. IHES Pubi. Math. 42 (1973) 323-395 [Rol] Roberts, P.: The vanishing of intersection multiplicities of perfect complexes. Bull. Amer.... more
... J. 28 (1981) 199-222 [PS] Peskine, G, Szpiro, L.: Dimension projective finie et cohomologie locale. IHES Pubi. Math. 42 (1973) 323-395 [Rol] Roberts, P.: The vanishing of intersection multiplicities of perfect complexes. Bull. Amer. Math. Soc. ...
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- ICMS소장학술지 - ICMS소장논문 - 학술지검색 - 전자학술지목록 - MSC - 원문복사서비스 - 투고요령. - 수학도서검색 - 국내외대학도서관 - 국외출판사. - 직접입력 - 외부입력. ...