Asymptotic behaviour

of Castelnuovo-Mumford regularity

Author:
Vijay Kodiyalam

Journal:
Proc. Amer. Math. Soc. **128** (2000), 407-411

MSC (1991):
Primary 13D02; Secondary 13D40

DOI:
https://doi.org/10.1090/S0002-9939-99-05020-0

Published electronically:
July 6, 1999

MathSciNet review:
1621961

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let be a polynomial ring over a field. For a graded -module generated in degree at most , the Castelnuovo-Mumford regularity of each of (i) its symmetric power, (ii) its torsion-free symmetric power and (iii) the integral closure of its torsion-free symmetric power is bounded above by a linear function in with leading coefficient at most . For a graded ideal of , the regularity of is given by a linear function of for all sufficiently large . The leading coefficient of this function is identified.

**[BrtEinLzr]**Aaron Bertram, Lawrence Ein, Robert Lazarsfeld,*Vanishing theorems, a theorem of Severi, and the equations defining projective varieties*, Journal of the American Mathematical Society**4**(1991), 587-602. MR**92g:14014****[Brt]**Aaron Bertram,*An application of a log version of the Kodaira vanishing theorem to embedded projective varieties*, Preprint alg-geom/9707001.**[Chn]**Karen A. Chandler,*Regularity of the powers of an ideal*, Communications in Algebra**25 (12)**(1997), 3773-3776. CMP**98:04****[Cnc]**Aldo Conca,*Hilbert function and resolutions of the powers of the ideal of the rational normal curve*, Preprint.**[CncHrzTrnVll]**Aldo Conca, Jurgen Herzog, Ngo Viet Trung, Giuseppe Valla,*Diagonal subalgebras of bigraded algebras and embeddings of blow-ups of projective spaces*, American Journal of Mathematics**119 (4)**(1997), 859-902. CMP**97:17****[CtkHrzTrn]**Dale Cutkosky, Jurgen Herzog, Ngo Viet Trung,*Asymptotic behaviour of the Catelnuovo-Mumford regularity*, Preprint.**[Snb]**David Eisenbud,*Commutative Algebra with a View Toward Algebraic Geometry*, Springer-Verlag, 1995. MR**97a:13001****[SnbGot]**David Eisenbud, Shiro Goto,*Linear free resolutions and minimal multiplicity*, Journal of Algebra**88**(1984), 89-133. MR**85f:13023****[GrmGmgPtt]**A. V. Geramita, A. Gimigliano, Y. Pitteloud,*Graded Betti numbers of some embedded rational n-folds*, Mathematische Annalen**301**(1995), 363-380. MR**96f:13022****[HoaTrn]**Le Tuan Hoa, Ngo Viet Trung,*On the Castelnuovo-Mumford regularity and the arithmetic degree of monomial ideals*, Mathematische Zeitschrift, To appear.**[Res]**D. Rees,*Reduction of modules*, Mathematical Proceedings of the Cambridge Philosophical Society**101**(1987), 431-448. MR**88a:13001****[SmtSwn]**Karen E. Smith, Irena Swanson,*Linear bounds on growth of associated primes*, Communications in Algebra,**25**(1997), 3071-3079. CMP**97:17****[Str]**Bernd Sturmfels,*Four counterexamples in combinatorial algebraic geometry*, Preprint.**[Swn]**Irena Swanson,*Powers of ideals: Primary decompositions, Artin-Rees lemma and regularity*, Mathematische Annalen**307**(1997), 299-313. MR**97j:13005**

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Additional Information

**Vijay Kodiyalam**

Affiliation:
The Institute of Mathematical Sciences, Chennai, India 600113

Email:
vijay@imsc.ernet.in

DOI:
https://doi.org/10.1090/S0002-9939-99-05020-0

Received by editor(s):
October 28, 1997

Received by editor(s) in revised form:
April 15, 1998

Published electronically:
July 6, 1999

Communicated by:
Wolmer V. Vasconcelos

Article copyright:
© Copyright 1999
American Mathematical Society