Castelnuovo–Mumford Regularity of Sums of Powers of Polynomial Ideals

REFERENCES

• Cutkosky , D. , Herzog , J. , Trung , N. V. ( 1999 ). Asymptotic behaviour of the Castelnuovo–Mumford regularity . Compositio Math. 118 : 243 – 261 .
   Web of Science ®Google Scholar
• Cutkosky , D. , Ein , L. , Lazarsfeld , R. ( 2001 ). Positivity and complexity of ideal sheaves . Math. Ann. 321 ( 2 ): 213 – 234 .
   Web of Science ®Google Scholar
• Eisenbud , D. ( 1995 ). Commutative Algebra. With a View Toward Algebraic Geometry . Graduate Texts in Mathematics, 150 . New York : Springer-Verlag .
   Google Scholar
• Hermiller , S. M. , Swanson , I. ( 2005 ). Computation with Frobenius powers . Experiment. Math. 14 : 161 – 173 .
   Web of Science ®Google Scholar
• Herzog , J. , Hoa , L. T. , Trung , N. V. ( 2002 ). Asymptotic linear bounds for the Castelnuovo–Mumford regularity . Trans. Amer. Math. Soc. 354 : 1793 – 1809 .
   Google Scholar
• Hoa , L. T. , Trung , N. V. ( 1998 ). On the Castelnuovo–Mumford regularity and the arithmetic degree of monomial ideals . Math. Z. 229 : 519 – 537 .
   Web of Science ®Google Scholar
• Hoa , L. T. , Trung , N. V. ( 2003 ). Borel-fixed ideals and reduction number . J. Algebra 270 : 335 – 346 .
   Web of Science ®Google Scholar
• Katzman , M. ( 1998 ). The complexity of Frobenius powers of ideals . J. Algebra 203 : 211 – 225 .
   Google Scholar
• Kodiyalam , V. ( 2000 ). Asymptotic behaviour of the Castelnuovo–Mumford regularity . Proc. Amer. Math. Soc. 50 : 407 – 411 .
   Google Scholar
• Kouchnirenko , A. G. ( 1976 ). Polyèdres de Newton et nombres de Milnor . Invent. Math. 32 : 1 – 31 .
   Web of Science ®Google Scholar
• Reid , L. , Roberts , L. G. , Vitulli , M. A. ( 2003 ). Some results on normal homogeneous ideals . Comm. Algebra 31 : 4485 – 4506 .
   Web of Science ®Google Scholar
• Rockafellar , R. T. ( 1970 ). Convex Analysis . Princeton : New Jersey Princeton University Press .
   Google Scholar
• Sjögren , R. ( 1992 ). On the regularity of graded k-algebras of Krull dimension ≤1 . Math. Scand. 71 : 167 – 172 .
   Google Scholar
• Trung , N. V. ( 1987 ). Reduction exponent and degree bound for the defining equations of graded rings . Proc. Amer. Math. Soc. 101 : 229 – 236 .
   Web of Science ®Google Scholar
• Trung , N. V. , Wang , H.-J. ( 2005 ). On the asymptotic linearity of Castelnuovo–Mumford regularity . J. Pure Appl. Algebra 201 : 42 – 48 .
   Google Scholar
• Communicated by I. Swanson.
   Google Scholar