The regularity of Tor and graded Betti numbers

American Journal of Mathematics

Volumn 128, Issue 3, 2006, Pages 573-605

  Eisenbud, David ^a   Huneke, Craig ^b   Ulrich, Bernd ^c  

^a MATHEMATICAL SCIENCES RESEARCH INSTITUTE   (United States)

^b UNIVERSITY OF KANSAS   (United States)

^c PURDUE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33745637245     PISSN: 00029327     EISSN: None     Source Type: Journal    
DOI: 10.1353/ajm.2006.0022     Document Type: Article

References (30)

1. M. Auslander, Modules over unramified regular local rings, Illinois J. Math. 5 (1961), 631-647.
2. L. Busé and M. Chardin, Implicitizing rational hypersurfaces using approximation complexes, J. Symbolic Compta. 40 (2005), 1150-1168.
3. L. Busé and J.-P. Jouanolou, On the closed image of a rational map and the implicitization problem, J. Algebra 265 (2003), 312-357.
4. G. Caviglia, Bounds on the Castelnuovo-Mumford regularity of tensor products, Proc. Amer. Math. Soc. (to appear), preprint, 2003.
5. _, Koszul algebras, Castelnuovo-Mumford regularity and generic initial ideals, Ph.D. thesis, University of Kansas, 2004.
6. K. Chandler, Regularity of the powers of an ideal, Comm. Algebra 25 (1997), 3773-3776.
7. A. Conca, Regularity jumps for powers of ideals, http://www.arxiv.org/ math.AC/0310493, 2003.
8. A. Conca and J. Herzog, Castelnuovo-Mumford regularity of products of ideals, Collect. Math. 54 (2003), 137-152.
9. A. Conca, J. Herzog and T. Hibi, Rigid resolutions and big Betti numbers, Comment. Math. Helv. 79 (2004), 826-839.
10. W. Decker, L. Ein and F.-O. Schreyer, Construction of surfaces in P4, J. Algebraic Geom. 2 (1993), 185-237.
11. D. Eisenbud, Linear sections of determinantal varieties, Amer. J. Math. 110 (1988), 541-575.
12. _, Commutative Algebra with a View Toward Algebraic Geometry, Springer-Verlag, New York, 1995.
13. _, The Geometry of Syzygies, Springer-Verlag, New York, 2005.
14. D. Eisenbud, M. Green, K. Hulek and S. Popescu, Restricting linear syzygies: algebra and geometry, Compositio Math. 141 (2005), 1460-1478.
15. W. Fulton and R. Lazarsfeld, On the connectedness of degeneracy loci and special divisors, Acta Math. 146 (1981), 271-283.
16. A. V. Geramita and A. Gimigliano, Generators for the defining ideal of certain rational surfaces, Duke Math. J. 62 (1991), 61-83.
17. A. V. Geramita, A. Gimigliano, and Y. Pitteloud, Graded Betti numbers of some embedded rational n-folds, Math. Ann. 301 (1995), 363-380.
18. S. Goto and Y. Shimoda, On the Rees algebras of Cohen-Macaulay local rings, Commutative Algebra (Fairfax, VA, 1979), Lecture Notes in Pure and Appl. Math., vol. 68, Dekker, New York, 1982, pp. 201-231.
19. D. Grayson and M. Stillman, Macaulay2, http://www.math.uiuc.edu/ Macaulay2/
20. R. Hartshorne, Ample Subvarieties of Algebraic Varieties, Notes written in collaboration with C. Musili, Lecture Notes in Math., vol. 156, Springer-Verlag, New York, 1970.
21. J. Herzog and T. Hibi, Castelnuovo-Mumford regularity of simplicial semigroup rings with isolated singularity, Proc. Amer. Math. Soc. 131 (2003), 2641-2647.
22. J. Herzog, T. Hibi and M. Vladoiu, Ideals of fiber type and polymatroids, preprint, 2003.
23. C. Huneke, Numerical invariants of liaison classes, Invent. Math. 75 (1984), 301-325.
24. 4, Proc. London Math. Soc. 76 (1998), 257-275.
25. S. Popescu and K. Ranestad, Surfaces of degree 10 in the projective four space via linear systems and linkage, J. Algebraic Geom. 5 (1996), 13-76.
26. T. G. Room, The Geometry of Determinantal Loci, Cambridge University Press, Cambridge, 1938.
27. J. Sidman, On the Castelnuovo-Mumford regularity of products of ideal sheaves, Adv. Geom. 2 (2002), 219-229.
28. B. Sturmfels, Four counterexamples in combinatorial algebraic geometry, J. Algebra 230 (2000), 282-294.
29. N. V. Trung and H.-J. Wang, On the asymptotic linearity of Castelnuovo-Mumford regularity, J. Pure Appl. Algebra 201 (2005), 42-48.
30. P. Valabrega and G. Valla, Form rings and regular sequences, Nagoya Math. J. 72 (1978), 93-101.