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Abstract:

An explicit lattice point realization is provided for the primary components of an arbitrary binomial ideal in characteristic zero. This decomposition is derived from a characteristic-free combinatorial description of certain primary components of binomial ideals in affine semigroup rings, namely those that are associated to faces of the semigroup. These results are intimately connected to hypergeometric differential equations in several variables. © Springer-Verlag 2009.

Registro:

Documento: Artículo
Título:Combinatorics of binomial primary decomposition
Autor:Dickenstein, A.; Matusevich, L.F.; Miller, E.
Filiación:Departamento de Matemática, FCEN, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Department of Mathematics, Texas A and M University, College Station, TX 77843, United States
Department of Mathematics, University of Minnesota, Minneapolis, MN 55455, United States
Department of Mathematics, Duke University, Durham, NC 27708, United States
Año:2010
Volumen:264
Número:4
Página de inicio:745
Página de fin:763
DOI: http://dx.doi.org/10.1007/s00209-009-0487-x
Título revista:Mathematische Zeitschrift
Título revista abreviado:Math. Z.
ISSN:00255874
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00255874_v264_n4_p745_Dickenstein

Referencias:

  • Bogart, T., Jensen, A., Thomas, R., The circuit ideal of a vector configuration (2007) J. Algebra, 309 (2), pp. 518-542
  • Cattani, E., Dickenstein, A., Counting solutions to binomial complete intersections (2007) J. Complexity, 23 (1), pp. 82-107
  • Dickenstein, A., Matusevich, L.F., Miller, E., Binomial D-modules, , Preprint. math. AG/0610353
  • Dickenstein, A., Matusevich, L.F., Sadykov, T., Bivariate hypergeometric D-modules (2005) Adv. Math., 196 (1), pp. 78-123
  • Eisenbud, D., Sturmfels, B., Binomial ideals (1996) Duke Math. J., 84 (1), pp. 1-45
  • Fischer, K.G., Shapiro, J., Mixed matrices and binomial ideals (1996) J. Pure Appl. Algebra, 113 (1), pp. 39-54
  • Gelfand, I.M., Graev, M.I., Zelevinskiǐ, A.V., Holonomic systems of equations and series of hypergeometric type (1987) Dokl. Akad. Nauk SSSR, 295 (1), pp. 14-19
  • Gel′fand, I.M., Zelevinskiǐ, A.V., Kapranov, M.M., Hypergeometric functions and toric varieties (1989) Funktsional. Anal. i Prilozhen, 23 (2), pp. 12-26. , (Correction in ibid, 27(4), 91 (1993))
  • Gilmer, R., Commutative semigroup rings (1984) Chicago Lectures in Mathematics, , University of Chicago Press, Chicago
  • Grayson, D.R., Stillman, M.E., Macaulay 2, A software system for research in algebraic geometry, , http://www.math.uiuc.edu/Macaulay2/, Available at
  • Hoşten, S., Shapiro, J., Primary decomposition of lattice basis ideals (2000) J. Symb. Comput., 29 (4-5), pp. 625-639. , (Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998))
  • Miller, E., Cohen-Macaulay quotients of normal semigroup rings via irreducible resolutions (2002) Math. Res. Lett., 9 (1), pp. 117-128
  • Matusevich, L.F., Miller, E., Walther, U., Homological methods for hypergeometric families (2005) J. Am. Math. Soc., 18 (4), pp. 919-941
  • Miller, E., Sturmfels, B., (2005) Combinatorial Commutative Algebra. Graduate Texts in Mathematics, 227. , New York: Springer
  • Greuel, G.-M., Pfister, G., Schönemann, H., (2005) Singular 3.0. A Computer Algebra System for Polynomial Computations, , http://www.singular.uni-kl.de, Centre for Computer Algebra, University of Kaiserslautern
  • Ojedamartínezde, C.I., Sánchez, R.P., Cellular binomial ideals. Primary decomposition of binomial ideals (2000) J. Symb. Comput., 30 (4), pp. 383-400
  • Saito, M., Sturmfels, B., Takayama, N., (2000) Gröbner Deformations of Hypergeometric Differential Equations, , Berlin: Springer
  • Sturmfels, B., (1996) Gröbner Bases and Convex Polytopes, , Providence: American Mathematical Society

Citas:

---------- APA ----------
Dickenstein, A., Matusevich, L.F. & Miller, E. (2010) . Combinatorics of binomial primary decomposition. Mathematische Zeitschrift, 264(4), 745-763.
http://dx.doi.org/10.1007/s00209-009-0487-x
---------- CHICAGO ----------
Dickenstein, A., Matusevich, L.F., Miller, E. "Combinatorics of binomial primary decomposition" . Mathematische Zeitschrift 264, no. 4 (2010) : 745-763.
http://dx.doi.org/10.1007/s00209-009-0487-x
---------- MLA ----------
Dickenstein, A., Matusevich, L.F., Miller, E. "Combinatorics of binomial primary decomposition" . Mathematische Zeitschrift, vol. 264, no. 4, 2010, pp. 745-763.
http://dx.doi.org/10.1007/s00209-009-0487-x
---------- VANCOUVER ----------
Dickenstein, A., Matusevich, L.F., Miller, E. Combinatorics of binomial primary decomposition. Math. Z. 2010;264(4):745-763.
http://dx.doi.org/10.1007/s00209-009-0487-x