F. Salem, S. Gao, and A. G. Lauder, Factoring polynomials via polytopes, proc. of ISSAC, pp.4-11, 2004.

M. Andersson, Residue currents and ideal of meromorphic functions, Bull. Sci. math, pp.481-512, 2004.

M. Avendano, T. Krick, and M. Sombra, Factoring bivariate sparse (lacunary) polynomials, J. of Complexity, vol.23, pp.193-216, 2007.
URL : https://hal.archives-ouvertes.fr/hal-00358830

K. Belabas, M. Van-hoeij, J. Klüners, and A. Steel, Factoring polynomials over global fields, J. of Symb. Comp, vol.40, pp.1325-1339, 2005.
URL : https://hal.archives-ouvertes.fr/hal-00440300

A. Bostan, G. Lecerf, B. Salvy, ´. E. Schost, and B. Wiebelt, Complexity issues in bivariate polynomial factorization, Proc. of ISSAC, pp.42-49, 2004.
URL : https://hal.archives-ouvertes.fr/hal-00186759

L. Busé and G. Chèze, On the total order of reducibility of a pencil of algebraic plane curves, 2008.

G. Chèze, Absolute polynomial factorization in two variables and the knapsack proble, proc. of ISSAC, pp.87-94, 2004.

G. Chèze and G. Lecerf, Lifting and recombination techniques for absolute factorization, J. of Complexity, vol.23, issue.3, pp.380-420, 2007.

D. Cox, Geometry of toric surfaces, vol.7, 2000.

V. Danilov, The geometry of toric varieties, Russian Math. Surveys, vol.33, pp.97-154, 1978.

M. Elkadi, A. Galligo, and M. Weimann, Towards Toric Absolute Factorization, J. Symb. Comp, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00438275

A. Galligo and D. Rupprecht, Irreducible decomposition of curves, J. Symb. Comp, vol.33, pp.661-677, 2002.

W. Fulton, Introduction to Toric Varieties, Annals of Math. Studies, 1993.

S. Gao, Factoring multivariate polynomials via partial differential equation, Math. Comp, vol.72, pp.801-822, 2003.

J. Zur-gathen and J. Gerhard, Modern computer algebra, 2003.

A. G. Khovansky, Newton polyhedra and toric varieties, Funct. Anal. Appl, vol.11, pp.56-67, 1977.

R. Lazarsfeld, Positivity in Algebraic Geometry I, 2005.

G. Lecerf, New recombination algorithms for bivariate polynomial factorization based on Hensel lifting, AAECC, vol.21, issue.2, pp.151-176, 2010.
URL : https://hal.archives-ouvertes.fr/hal-00157496

G. Lecerf, Sharp precision in Hensel lifting for bivariate polynomial factorization, Math. of Comp, vol.75, pp.921-933, 2006.
URL : https://hal.archives-ouvertes.fr/hal-00186733

A. K. Lenstra, H. W. Lenstra, J. , and L. Lovasz, Factoring Polynomials with Rational Coefficients, Math. Ann, vol.261, issue.2, pp.515-534, 1982.

A. Novocin, Factoring Univariate Polynomials over the Rationals, 2008.

A. M. Ostrowski, On multiplication and factorization of polynomials. Lexicographic orderings and extreme aggregates of terms, Aequationes Math, vol.13, pp.201-228, 1975.

. Reduzibilität-ebener-kurven, J. Reine Angew. Math, vol.369, pp.167-191, 1986.

A. Storjohann, Algorithms for matrix canonical forms, 2000.

C. Voisin, Théorie de Hodge et géométrie algébrique complexe, SMF, 2004.

M. Weimann, La trace en géométrie projective et torique, Université de Bordeaux, vol.1, 2006.

M. Weimann, An interpolation theorem in toric varieties, Ann. Inst. Fourier, vol.58, issue.4, pp.1371-1381, 2008.
URL : https://hal.archives-ouvertes.fr/hal-00136120

M. Weimann, Algebraic osculation and factorization of sparse polynomials, 2009.
URL : https://hal.archives-ouvertes.fr/hal-02137318

, Departament Algebra i Geometria, Facultat de Matemàtiques, Universitat Barcelona Gran via 585, 08007 Barcelona. E-mail address