Martín Sombra: publications and other math texts


        Publications listed at MathSciNet (MR Author ID: 621582) and at Zentralbatt MATH
        Preprints posted at arXiv
        Citations at Google Scholar

          Research monograph

Astérisque 360
    1. J. I. Burgos Gil, P. Philippon, and M. Sombra, Arithmetic geometry of toric varieties. Metrics, measures and heights, Astérisque 360, Société Mathématique de France, 2014, vi + 222 pages, ISBN 978-2-85629-783-4.

Research papers

    1. M. Sombra and A. Yger, Bounds for multivariate residues and for the polynomials in the elimination theorem, submitted, 40 pages.
    2. M.-C. Chang, C. D'Andrea, A. Ostafe, I. E. Shparlinski, and M. Sombra, Orbits of polynomial dynamical systems modulo primes, to appear in Proceedings of the American Mathematical Society, 11 pages.
    3. C. Martínez and M. Sombra, An arithmetic Bernstein-Kushnirenko inequality, submitted, 32 pages.
    4. C. D'Andrea, M. Narváez-Clauss, and M. Sombra, Quantitative equidistribution of Galois orbits of small points in the N-dimensional torus, to appear in Algebra & Number Theory, 23 pages.
    5. J. I. Burgos Gil, P. Philippon, J. Rivera-Letelier, and M. Sombra, The distribution of Galois orbits of points of small height in toric varieties, submitted, 52 pages.
    6. C. D'Andrea, A. Ostafe, I. E. Shparlinski, and M. Sombra, Reduction modulo primes of systems of polynomial equations and algebraic dynamical systems, submitted, 41 pages.
    7. F. Amoroso, M. Sombra, and U. Zannier, Unlikely intersections and multiple roots of sparse polynomials, Mathematische Zeitschrift (2017), DOI 10.1007/s00209-017-1860-9, 17 pages.
    8. J. I. Burgos Gil, P. Philippon, and M. Sombra, Height of varieties over finitely generated fields, Kyoto Journal of Mathematics 56 (2016) 13-32.
    9. S. Basu and M. Sombra, Polynomial partitioning on varieties of codimension two and point-hypersurface incidences in four dimensions, Discrete & Computational Geometry 55 (2016) 158-184.
    10. J. I. Burgos Gil, A. Moriwaki, P. Philippon, and M. Sombra, Arithmetic positivity on toric varieties, Journal of Algebraic Geometry 25 (2016) 201-272.
    11. J. I. Burgos Gil, P. Philippon, and M. Sombra, Height of toric varieties, entropy and integration over polytopes, in F. Nielsen and F. Barbaresco (eds.), "Geometric Science of Information", Lecture Notes in Computer Science 9389 (2015) 286-295.
    12. J. I. Burgos Gil, P. Philippon, and M. Sombra, Successive minima of toric height functions, Annales de l'Institut Fourier (Grenoble) 65 (2015), 2145-2197.
    13. C. D'Andrea and M. Sombra, A Poisson formula for the sparse resultant, Proceedings of the London Mathematical Society 11 (2015) 932-964.
    14. F. Amoroso, L. Leroux, and M. Sombra, Overdetermined systems of sparse polynomial equations, Foundations of Computational Mathematics 15 (2015) 53-87.
    15. C. D'Andrea, A. Galligo, and M. Sombra, Quantitative equidistribution for the solutions of a system of sparse polynomial equations, American Journal of Mathematics 136 (2014) 1543-1579.
    16. C. D'Andrea, T. Krick, and M. Sombra, Height of varieties in multiprojective spaces and arithmetic Nullstellensätze, Annales Scientifiques de l'École Normale Supérieure 46 (2013) 549-627.
    17. J. I. Burgos Gil and M. Sombra, When do the recession cones of a polyhedral complex form a fan?, Discrete & Computational Geometry 46 (2011) 789-798.
    18. C. D'Andrea and M. Sombra, The Newton polygon of a rational plane curve, Mathematics in Computer Science 4 (2010) 3-24.
    19. J. I. Burgos Gil, P. Philippon, and M. Sombra, Hauteur des sous-schémas toriques et dualité de Legendre-Fenchel, Comptes Rendus Mathématique 347 (2009) 589-594.
    20. P. Philippon and M. Sombra, A refinement of the Bernstein-Kushnirenko estimate, Advances in Mathematics 218 (2008) 1370-1418.
    21. P. Philippon and M. Sombra, Minimum essentiel et degrés d'obstruction des translatés de sous-tores, Acta Arithmetica 133 (2008) 1-24.
    22. P. Philippon and M. Sombra, Quelques aspects diophantiens des variétés toriques projectives, in R. F. Tichy, H. P. Schlickewei, and K. Schmidt (eds.), "Diophantine Approximation: Festschrift for Wolfgang Schmidt". Developments in Mathematics 16 (2008) 295-338.
    23. P. Philippon and M. Sombra, Hauteur normalisée des variétés toriques projectives, Journal of the Institute of Mathematics of Jussieu 7 (2008) 327-373.
    24. M. Avendaño, T. Krick, and M. Sombra, Factoring bivariate sparse (lacunary) polynomials, Journal of Complexity 23 (2007) 193-216. This paper received the Journal of Complexity Best Paper Award.
    25. P. Philippon and M. Sombra, Une nouvelle majoration pour le nombre de solutions d'un système d'équations polynomiales, Comptes Rendus Mathématique 345 (2007) 335-340.
    26. P. Philippon and M. Sombra, Géométrie diophantienne et variétés toriques, Comptes Rendus Mathématique 340 (2005) 507-512.
    27. C. D'Andrea and M. Sombra, Определитель Кэли — Менгера неприводим при n≥3, Sibirskij Matematicheskij Zhurnal 46 (2005) 90-97. English translation: The Cayley-Menger determinant is irreducible for n≥3. Siberian Mathematical Journal 46 (2005) 71-76,
    28. M. Sombra, Minimums successifs des varietes toriques projectives, Journal für die Reine und Angewandte Mathematik 586 (2005) 207-233.
    29. M. Sombra, The height of the mixed sparse resultant, American Journal of Mathematics 126 (2004) 1253-1260.
    30. G. Jeronimo, T. Krick, J. Sabia, and M. Sombra, The computational complexity of the Chow form, Foundations of Computational Mathematics 4 (2004) 41-117.
    31. A. J. Di Scala and M. Sombra, Intrinsic palindromes, The Fibonacci Quarterly 42 (2004) 76-81.
    32. T. Krick, L. M. Pardo, and M. Sombra, Sharp estimates for the arithmetic Nullstellensatz, Duke Mathematical Journal 109 (2001) 521-598. This paper received an AMS Featured Review.
    33. K. Hägele, J. E. Morais, L. M. Pardo, and M. Sombra, On the intrinsic complexity of the arithmetic Nullstellensatz, Journal of Pure and Applied Algebra 146 (2000) 103-183.
    34. M. Sombra, A sparse effective Nullstellensatz, Advances in Applied Mathematics 22 (1999) 271-295.
    35. M. Sombra, Bounds for the Hilbert function of polynomial ideals and for the degrees in the Nullstellensatz, Journal of Pure and Applied Algebra 117 & 118 (1997) 565-599.

Expository texts

  1. C. D'Andrea and M. Sombra, Rational parametrizations, intersection theory and Newton polytopes, in I. Emiris, F. Sottile & T. Theobald (eds.), "Non-linear computational geometry", IMA Volumes in Mathematics and its Applications 151 (2009) 35-50.
  2. C. D'Andrea and M. Sombra, Sobre curvas paramétricas y polígonos de Newton, Gaceta de la Real Sociedad Matemática Española 11 (2008) 317-336. Catalan translation: Sobre corbes paramètriques i polígons de Newton, Butlletí de la Societat Catalana de Matemàtiques 23 (2008) 201–219.


  1. M. Sombra, Estimaciones para el teorema de ceros de Hilbert, Ph.D. Thesis, Universidad de Buenos Aires, 1998, viii+125 pages. 
  2. M. Sombra, Fórmulas de traza en la teoría de funciones L, Master Thesis, Universidad de La Plata, 1993, 49 pages.

Edition of conference proceedings

  1. J. Elias, J. Fernández Sánchez, and M. Sombra (eds.), Encuentros de álgebra computacional y aplicaciones (EACA 2014) , Barcelona, 2014, 178 pages, ISBN 978-84-697-0651-0.


Francesco Amoroso (U. Caen), Martín Avendaño (U. Zaragoza), Saugata Basu (Purdue U.), José Ignacio Burgos Gil (ICMAT, Madrid), Mei-Chu Chang (U. California at Riverside), Carlos D'Andrea (U. Barcelona), Antonio Di Scala (Politecnico di Torino), André Galligo (U. Nice), Klemens Hagele, Gabriela Jeronimo (U. Buenos Aires), Teresa Krick (U. Buenos Aires), Louis Leroux (U. Caen), César Martínez (U. Caen), José Enrique Morais (U. Alcalá), Atsushi Moriwaki (Kyoto U.), Marta Narváez-Clauss (U. Barcelona), Alina Ostafe (U. New South Wales), Luis Miguel Pardo (U. Cantabria, Santander), Patrice Philippon (IMJ, Paris), Juan Rivera-Letelier (Rochester U.), Juan Sabia (U. Buenos Aires), Igor Shparlinski (U. New South Wales), Alain Yger (U. Bordeaux), Umberto Zannier (Scuola Normale, Pisa)

Last update: 20 August 2017