Artículo

Este artículo es de Acceso Abierto y puede ser descargado en su versión final desde nuestro repositorio
Consulte el artículo en la página del editor
Consulte la política de Acceso Abierto del editor

Abstract:

We present examples that show that in dimension higher than one or codimension higher than two, there exist toric ideals IA such that no binomial ideal contained in IA and of the same dimension is a complete intersection. This result has important implications in sparse elimination theory and in the study of the Horn system of partial differential equations. © 2006 American Mathematical Society.

Registro:

Documento: Artículo
Título:Complete intersections in toric ideals
Autor:Cattani, E.; Curran, R.; Dickenstein, A.
Filiación:Department of Mathematics and Statistics, University of Massachusetts, Amherst, MA 01003, United States
Department of Mathematical and Computer Sciences, Metropolitan State College of Denver, Denver, CO 80202, United States
Departamento de Matematica, FCEyN, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Año:2007
Volumen:135
Número:2
Página de inicio:329
Página de fin:335
DOI: http://dx.doi.org/10.1090/S0002-9939-06-08513-3
Título revista:Proceedings of the American Mathematical Society
Título revista abreviado:Proc. Am. Math. Soc.
ISSN:00029939
PDF:https://bibliotecadigital.exactas.uba.ar/download/paper/paper_00029939_v135_n2_p329_Cattani.pdf
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00029939_v135_n2_p329_Cattani

Referencias:

  • Barile, M., Morales, M., Thoma, A., On simplicial toric varieties which are set-theoretic complete intersections (2000) J. Algebra, 226 (2), pp. 880-892. , MR1752767 (2001i:14066)
  • Barile, M., Morales, M., Thoma, A., Geometric and combinatorial aspects of commutative algebra (Messina, 1999) (2001) Lecture Notes in Pure and Appl. Math., 217, pp. 1-9. , On free complete intersections, Dekker, New York, MR1824213 (2002c:13026)
  • Barile, M., Morales, M., Thoma, A., Set-theoretic complete intersections on binomials (2002) Proc. Amer. Math. Soc., 130 (7), pp. 1893-1903. , MR1896020 (2003f:14058)
  • CoCoA: A System for Doing Computations in Commutative Algebra, , http://cocoa.dima.unige.it, CoCoATeam, Available at
  • Delorme, C., Sous-monoïdes d'intersection complète de (1976) N. Ann. Sci. École Norm. Sup. (4), 9 (1), pp. 145-154. , MR0407038 (53:10821)
  • Dickenstein, A., Matusevich, L.F., Sadykov, T., Bivariate hypergeometric D-modules (2005) Advances in Mathematics, 196 (1), pp. 78-123. , DOI 10.1016/j.aim.2004.08.012, PII S0001870804002828
  • Dickenstein, A., Sturmfels, B., Elimination theory in codimension 2 (2002) J. Symbolic Comput., 34, pp. 119-135. , MR1930829 (2003h:14073)
  • Eisenbud, D., Sturmfels, B., Binomial ideals (1996) Duke Mathematical Journal, 84 (1), pp. 1-45. , DOI 10.1215/S0012-7094-96-08401-X
  • Fischer, K.G., Morris, W., Shapiro, J., Affine semigroup rings that are complete intersections (1997) Proceedings of the American Mathematical Society, 125 (11), pp. 3137-3145
  • Fischer, K.G., Morris, W., Shapiro, J., Mixed Dominating Matrices (1998) Linear Algebra and Its Applications, (270), pp. 191-214
  • Fischer, K.G., Shapiro, J., Mixed matrices and binomial ideals (1996) Journal of Pure and Applied Algebra, 113 (1), pp. 39-54. , DOI 10.1016/0022-4049(95)00144-1
  • Gel'fand, I.M., Kapranov, M.M., Zelevinsky, A.V., (1994) Discriminants, Resultants and Multidimensional Determinants, , Birkhäuser, Boston, MR1264417 (95e:14045)
  • Herzog, J., Generators and relations of abelian semigroups and semigroup rings (1970) Manuscripta Math., 3, pp. 175-193. , MR0269762 (42:4657)
  • Hoşten, S., Shapiro, J., Primary decomposition of lattice basis ideals (2000) J. Symbolic Comput., 29 (4-5), pp. 625-639. , Symbolic computation in algebra, analysis, and geometry (Berkeley, CA, 1998). MR1769658 (2001h:13012)
  • Nakajima, H., Affine torus embeddings which are complete intersections (1986) Tohoku Math. J. (2), 38 (1), pp. 85-98. , MR0826766 (87c:14058)
  • Rosales, J.C., Garćia-Sánchez, P.A., On complete intersection affine semigroups (1995) Comm. Algebra, 23 (14), pp. 5395-5412. , MR1363611 (96m:14068)
  • Scheja, G., Scheja, O., Storch, U., On regular sequences of binomials (1999) Manuscripta Math, 98 (1), pp. 115-132. , MR1669583 (99k:13017)
  • Stanley, R.P., Relative invariants of finite groups generated by pseudoreflections (1977) J. Algebra, 49 (1), pp. 134-148. , MR0460484 (57:477)
  • Sturmfels, B., (1996) Gröbner Bases and Convex Polytopes, 8. , University Lecture Series, American Mathematical Society, Providence, RI, MR1363949 (97b:13034)
  • Thoma, A., Construction of set theoretic complete intersections via semigroup gluing (2000) Beiträge Algebra Geom., 41 (1), pp. 195-198. , MR1745589 (2001h:14059)
  • Thoma, A., On the binomial arithmetical rank (2000) Arch. Math. (Basel), 74 (1), pp. 22-25. , MR1728358 (2001a:14023)
  • Watanabe, K., Invariant subrings which are complete intersections. I. Invariant subrings of finite abelian groups (1980) Nagoya Math. J., 77, pp. 89-98. , MR0556310 (82d:13020)
  • Ziegler, G.M., (1995) Lectures on Polytopes, , Springer, New York, MR1311028 (96a:52011)

Citas:

---------- APA ----------
Cattani, E., Curran, R. & Dickenstein, A. (2007) . Complete intersections in toric ideals. Proceedings of the American Mathematical Society, 135(2), 329-335.
http://dx.doi.org/10.1090/S0002-9939-06-08513-3
---------- CHICAGO ----------
Cattani, E., Curran, R., Dickenstein, A. "Complete intersections in toric ideals" . Proceedings of the American Mathematical Society 135, no. 2 (2007) : 329-335.
http://dx.doi.org/10.1090/S0002-9939-06-08513-3
---------- MLA ----------
Cattani, E., Curran, R., Dickenstein, A. "Complete intersections in toric ideals" . Proceedings of the American Mathematical Society, vol. 135, no. 2, 2007, pp. 329-335.
http://dx.doi.org/10.1090/S0002-9939-06-08513-3
---------- VANCOUVER ----------
Cattani, E., Curran, R., Dickenstein, A. Complete intersections in toric ideals. Proc. Am. Math. Soc. 2007;135(2):329-335.
http://dx.doi.org/10.1090/S0002-9939-06-08513-3