Journal of Commutative Algebra

Some variants of Macaulay's and Max Noether's theorems

Elizabeth Wulcan

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J. Commut. Algebra, Volume 2, Number 4 (2010), 567-580.

First available in Project Euclid: 13 December 2010

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Wulcan, Elizabeth. Some variants of Macaulay's and Max Noether's theorems. J. Commut. Algebra 2 (2010), no. 4, 567--580. doi:10.1216/JCA-2010-2-4-567.

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  • M. Andersson, Residue currents and ideals of holomorphic functions, Bull. Sci. Math. 128 (2004), 481-512.
  • ––––, The membership problem for polynomial ideals in terms of residue currents, Ann. Inst. Fourier 56 (2006), 101-119.
  • M. Andersson and E. Götmark, Explicit representation of membership of polynomial ideals, Math. Ann., to appear.
  • M. Andersson and E. Wulcan, Residue currents with prescribed annihilator ideals, Ann. Sci. École Norm. Sup. 40 (2007), 985-1007.
  • ––––, Decomposition of residue currents, J. Reine angew. Math. 638 (2010), 103-118.
  • ––––, On the membership problem on algebraic varieties, in preparation.
  • C.A. Berenstein, R. Gay, A. Vidras and A. Yger, Residue currents and Bezout identities, Progress Math. 114, Birkhäuser Verlag, Berlin, 1993.
  • J-E. Björk, Residues and $\cal D$-modules, The legacy of Niels Henrik Abel, 605-651, Springer, Berlin, 2004.
  • J. Briançon and H. Skoda, Sur la clôture intégrale d'un idéal de germes de fonctions holomorphes en un point de $\C^n$, C.R. Acad. Sci. Paris 278 (1974), 949-951.
  • W. Castryck, J. Denef and F. Vercauteren, Computing zeta functions of nondegenerate curves, IMRP Int. Math. Res. Pap. 2006, Art. ID 72017, 57 pp.
  • N. Coleff and M. Herrera, Les courants résiduels associcés à une forme méromorphe, Lect. Notes Math. 633, Springer Verlag, Berlin, 1978.
  • D. Cox, The homogeneous coordinate ring of a toric variety, J. Algebraic Geom. 4 (1995), 17-50.
  • A. Dickenstein and C. Sessa, Canonical representatives in moderate cohomology, Invent. Math. 80 (1985), 417-434.
  • D. Eisenbud, Commutative algebra. With a view toward algebraic geometry, Grad. Texts Math. 150, Springer-Verlag, New York, 1995.
  • G. Ewald, Combinatorial convexity and algebraic geometry, Grad. Texts Math. 168, Springer-Verlag, New York, 1996.
  • W. Fulton, Introduction to toric varieties, Annals Math. Stud. 131, The William H. Roever Lectures in Geometry, Princeton University Press, Princeton, NJ, 1993.
  • M. Hickel, Solution d'une conjecture de C. Berenstein-A. Yger et invariants de contact à l'infini, Ann. Inst. Fourier 51 (2001), 707-744.
  • Z. Jelonek, On the effective Nullstellensatz, Invent. Math. 162 (2005), 1-17.
  • J. Kollár, Sharp effective Nullstellensatz, J. Amer. Math. Soc. 1 (1988), 963-975.
  • R. Lazarsfeld, Positivity in algebraic geometry. I. Classical setting: Line bundles and linear series, Springer-Verlag, Berlin, 2004.
  • ––––, Positivity in algebraic geometry. II. Positivity for vector bundles, and multiplier ideals, Springer-Verlag, Berlin, 2004.
  • F.S. Macaulay, The algebraic theory of modular systems, Cambridge University Press, Cambridge, 1916.
  • M. Nöther, Über einen Satz aus der Theorie der algebraischen Functionen, Math. Ann. 6 (1873), 351-359.
  • M. Passare, Residues, currents, and their relation to ideals of holomorphic functions, Math. Scand. 62 (1988), 75-152.
  • M. Passare, A. Tsikh and A. Yger, Residue currents of the Bochner-Martinelli type, Publ. Mat. 44 (2000), 85-117.
  • M. Sombra, A sparse effective Nullstellensatz, Adv. Appl. Math. 22 (1999), 271-295.
  • J. Tuitman, A refinement of a mixed sparse effective Nullstellensatz, IMRN, to appear.
  • E. Wulcan, Sparse effective membership problems via residue currents, Math. Ann., to appear.