The Limiting Shape of the Generic Initial System of a Complete Intersection

REFERENCES

• Ahn , J. , Migliore , J. C. ( 2007 ). Some geometric results arising from the Borel fixed property . J. Pure and Applied Algebra 209 : 337 – 360 .
   Web of Science ®Google Scholar
• Blickle , M. , Lazarsfeld , R. ( 2004 ). An informal introduction to multiplier ideals . In: Avramov , L. L. , Green , M. , Huneke , C. , Smith , K. E. , Sturmfels , B. , eds. Trends in Commutative Algebra. Vol. 51. MSRI Publications, pp. 87–114 .
   Google Scholar
• Bayer , D. , Stillman , M. ( 1987 ). A criterion for detecting m-regularity . Inventiones Mathematicae 87 : 1 – 11 .
   Web of Science ®Google Scholar
• Cimpoeaş , M. ( 2007 ). Generic initial ideal for complete intersections of embedding dimension three with strong Lefschetz property . Bull. Math. Soc. Sci. Math. Roum. (N. S.) 50 ( 98)(1 ): 33 – 66 .
   Web of Science ®Google Scholar
• Cho , Y. H. , Park , J. P. ( 2008 ). Conditions for generic initial ideals to be almost reverse lexicographic . J. Algebra 319 ( 7 ): 2761 – 2771 .
   Web of Science ®Google Scholar
• Eisenbud , D. ( 2004 ). Commutative Algebra with a View Toward Algebraic Geometry. Vol. 150 of Graduate Texts in Mathematics. Springer .
   Google Scholar
• Eliahou , S. , Kervaire , M. (1990). Minimal resolutions of some monomial ideals. J. Algebra 129:1–25.
   Web of Science ®Google Scholar
• Ein , L. , Lazarsfeld , R. , Smith , K. E. ( 2001 ). Uniform bounds and symbolic powers on smooth varieties . Inventiones Mathematicae 144 ( 2 ): 241 – 252 .
   Web of Science ®Google Scholar
• Ein , L. , Lazarsfeld , R. , Smith , K. E. ( 2003 ). Uniform approximation of Abhyankar valuation ideals in smooth function fields . Amer. J. Math. 125 : 409 – 440 .
   Web of Science ®Google Scholar
• Eisenbud , D. , Schreyer , F. O. ( 2009 ). Betti numbers of graded modules and cohomology of vector bundles . J. Amer. Math. Soc. 22 ( 3 ): 859 – 888 .
   Web of Science ®Google Scholar
• Galligo , A. ( 1974 ). A propos du théorem de préparation de Weierstrass . Lecture Notes in Mathematics 409 : 543 – 579 .
   Google Scholar
• Green , M. ( 1998 ). Generic initial ideals . In: Elias , J. , Giral , J. M. , Miro-Roig , R. M. , Zarzuela , S. , eds. Six Lectures on Commutative Algebra. Springer , pp. 119 – 186 .
   Google Scholar
• Grayson , D. R. , Stillman , M. E. Macaulay2, a software system for research in algebraic geometry. Available at http://www.math.uiuc.edu/Macaulay2/Accessed October 1, 2013.
   Google Scholar
• Guardo , E. , Tuyl , A. V. ( 2005 ). Powers of complete intersections: gradBetti numbers and applications . Illinois J. Math. 49 ( 1 ): 265 – 279 .
   Web of Science ®Google Scholar
• Howald , J. ( 2001 ). Multiplier ideals of monomial ideals . Trans. Amer. Math. Soc. 353 : 2665 – 2671 .
   Web of Science ®Google Scholar
• Herzog , J. , Srinivasan , H. ( 1998 ). Bounds for multiplicities . Trans. Amer. Math. Soc. 350 ( 7 ): 2879 – 2902 .
   Web of Science ®Google Scholar
• Huneke , C. ( 1992 ). Uniform bounds in Noetherian rings . Inventiones Mathematicae 107 ( 1 ): 203 – 233 .
   Web of Science ®Google Scholar
• Lax , P. D. ( 1996 ). Linear Algebra . Pure and Applied Mathematics . Hoboken , New Jersey : Wiley-Interscience .
   Google Scholar
• Lazarsfeld , R. K. ( 2004 ). Positivity in Algebraic Geometry I. Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics. Springer-Verlag .
   Google Scholar
• Mayes , S. ( 2013 ). The Generic Initial System of a 2-complete Intersection, arXiv:1206.5750v1[math.AC] .
   Google Scholar
• Migliore , J. , Nagel , U. ( 2011 ). A Tour of the Weak and Strong Lefschetz Properties. arXiv:1109.5718v2 [math.AC] .
   Google Scholar
• Mustaţă , M. ( 2002 ). On multiplicities of graded sequences of ideals . J. Algebra 256 : 229 – 249 .
   Web of Science ®Google Scholar
• Siu , Y.-T. ( 2001 ). Very ampleness part of Fujitas conjecture and multiplier ideal sheaves of Kohn and Nadel . In: McNeal , J. D. , eds. Complex Analysis and Geometry . Vol. 9. Ohio State University Mathematical Research Institute Publications. Verlag Walter de Gruyter, pp. 171–191 .
   Google Scholar
• Communicated by I. Swanson.
   Google Scholar