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Antonio Campillo

A Portrayal of His Life and Work

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Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics

Abstract

The main purpose is to present a biographical portrayal of Antonio Campillo López. In addition to the most relevant aspects of his life and academic career, we offer a panoramic view of his scientific work in fields such as singularity theory, commutative algebra, algebraic geometry, or coding theory. We also stress that his endeavors have been closely linked to an important work of research training, from which a thriving school has emerged. Finally, his vision and influence will be considered through his numerous institutional and scientific policy responsibilities at all levels.

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Notes

  1. 1.

    Constituted by Daniel Miguel San José, rector of the UVA; Pablo Raphael de la Madrid, Director of the Cultural Institute of the Embassy of Mexico in Spain; Gelasio Salazar Anaya, President of the SMM; Francisco Marcellán Español, President of the RSME; and by Edgar Martínez Moro, President of the Organizing Committee of the meeting.

  2. 2.

    “Antonio Campillo, bosquejos sobre su vida y obra”, by S. Xambó (https://mat-web.upc.edu/people/sebastia.xambo/Bios/AC/2017-Xambo--s-AC.pdf)

  3. 3.

    http://www.arbolmat.com/. Since February 2018, however, ArbolMat belongs solely to RSME and its name is RSME Gallery of Mathematics, Science and Technology.

  4. 4.

    http://www.arbolmat.com/antonio-campillo/

  5. 5.

    Licenciatura en Matemáticas. It was equivalent, roughly speaking, to a master’s degree in Mathematics in todays terms.

  6. 6.

    Formación de Personal Investigador, i.e. Training of Research Personel.

  7. 7.

    Singularities of algebroid plane curves in positive characteristic.

  8. 8.

    Ce livre très clair, définissant tous les concepts qu’il utilise, constitue une excellente introduction à l’aspect algébrique de la classification des singularités des courbes algébroïdes (ou analytiques complexes) irréductibles, en charactéristique positive comme en caractéristique zéro. […] Ici l’outil central est le développement de Hamburger-Noether […] en plus de l’extension à la caractéristique positive, ce livre est utile par la comparison soigneuse qu’il contient entre les différents systèmes d’invariants attachés à une singularité de branche: Hamburger-Noether, Puiseux, suite de multiplicités de points infiniment voisins, semigroupe des valuations, […] On trouve aussi le lien très utile après les travaux récents de Abhyankar entre le développement de Hamburger-Noether et la théorie du contact maximal d’une branche avec d’autres branches singulières […] Le dernier chapitre étudie trois définitions possibles de l’équisingularité des branches non planes.

  9. 9.

    W. Decker, G.-M. Greuel, G. Pfister, and H. Schönemann: Singular 4-1-0 —A computer algebra system for polynomial computations, 2016. http://www.singular.uni-kl.de

  10. 10.

    F. Pham, B. Teissier: Fractions lipschitziennes d’un algèbre analytique complexe et saturation de Zariski. Actes du Congrès International des Mathematiciens, Nice (1970), Tome 2, Gauthier-Villars, Paris (1971).

  11. 11.

    A factorization theorem for the polar of a curve with two branches. Composition Mathematica 92/3 (1994), 327–375.

  12. 12.

    C. Galindo and F. Monserrat: Algebraic integrability of foliations of the plane, Journal of Differential Equations 231/2 (2006), 611–632.

  13. 13.

    The cone of curves associated to a plane configuration, Commentarii Mathematici Helvectici 80/1 (2005), 75–93.

  14. 14.

    On the cone of curves and of line bundles of a rational surface, International Journal of Mathematics 15/4 (2004), 393–407.

  15. 15.

    F. Monserrat: Curves having one place at infinity and linear systems on rational surfaces, Journal of Pure and Applied Algebra 211/3 (2007), 685–701.

  16. 16.

    D. Le Brigand and J. J. Risler: Algorithme de Brill-Noether et codes de Goppa, Bull. Soc. math. France, 116/2 (1988), 231–253.

  17. 17.

    M. Carnicer: The Poincaré problem in the nondicritical case, Annals of Mathematics 140/2 (1994), 289–294.

  18. 18.

    Agencia Nacional de Evaluación y Prospectiva, ANEP.

  19. 19.

    Ministerio de Ciencia y Tecnología, MCyT. The Plan was coordinated by the Government Presidency.

  20. 20.

    Conferencia de Decanos de Matemáticas, CDM

  21. 21.

    Agencia Nacional de Evaluación de la Calidad y Acreditación, ANECA.

  22. 22.

    Societat Catalana de Matemàtiques, Sociedad Española de Matemática Aplicada, and Sociedad de Estadística e Investigación Operativa.

  23. 23.

    Comité Español de Matemáticas, http://matematicas.uclm.es/cemat/

  24. 24.

    http://www.arbolmat.com/ (cf. Footnote 3).

  25. 25.

    Belgian Mathematical Society/Société Mathématique de Belgique, and Société Mathématique du Luxembourg.

  26. 26.

    In recent years these include the habilitation and acreditation procedures.

  27. 27.

    http://iberoamericangeometry2018.uva.es/

  28. 28.

    2009: 12/4, 613–5. 2010: 13/1, 5–6; 13/2, 203–5; 13/3, 405–7; 13/4, 603–4. 2011: 14/2, 209–10; 14/3, 403–7; 14/4, 611–2. 2012: 15/1, 5–8; 15/2, 233–4; 15/3, 415–8. 2013: 16/1, 5–8; 16/2, 205–7; 16/4, 605–9. 2014: 17/1, 5–8; 17/2, 203–6; 17/3, 405–6; 17/4, 611–3. 2015: 18/, 7–10; 18/2, 219–21.

  29. 29.

    In this issue the piece is an interesting interview by Ann Lemahieu of María Pe Pereira, winner of the 2012 edition of the José Luis Rubio de Francia Prize.

  30. 30.

    Luis Español, Historia de la RSME. RSME, November 2011.

  31. 31.

    http://www.rsme.es/org/DeclaracionRSME291111.pdf

  32. 32.

    https://en.wikipedia.org/wiki/BBVA_Foundation_Frontiers_of_Knowledge_Award

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  21. Gusein-Zade, S., Delgado, F., Campillo, A.: Universal abelian covers of rational surface singularities, and multi-index filtrations. Funct. Anal. Its Appl. 42(2), 83–88 (2008)

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  29. Campillo, A., Delgado, F., Gusein-Zade, S.: An equivariant Poincaré series of filtrations and monodromy zeta functions. Revista Matemática Complutense 28(2), 449–467 (2015)

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  40. Campillo, A., Reguera, A.: Combinatorial aspects of sequences of point blowing ups. Manuscripta Mathematica 84(1), 29–46 (1994)

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  45. Campillo, A., Farrán, J.I.: Construction of AG-codes from symbolic Hamburger-Noether expressions of plane curves. Math. Comput. 71(240), 1759–1780 (2002)

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  49. Campillo, A., Lemahieu, A.: Poincaré series for filtrations defined by discrete valuations with arbitrary center. J. Algebra 377, 66–75 (2013)

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  55. Campillo, A., Pisón, P.: Generators for a monomial curve and graphs for the associated semigroup. Bull. Belg. Math. Soc. Série A 45(1–2), 45–58 (1993)

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  56. Campillo, A., Pisón, P.: L’ideal d’un semigroup de type fini. Comptes Rendus de l’Académie de Sciences – Série I – Mathématiques 316, 1303–1306 (1993)

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  60. Briales, A., Campillo, A., Pisón, P., Vignerón, A.: Minimal resolution of lattices and integer linear programing. Revista Matemática Iberoamericana 19(2), 287–306 (2003)

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  61. Campillo, A., Gonzalez-Sprinberg, G.: On characteristic cones, clusters and chains of infinitely near points. In: Brieskorn Anniversary Volume. Volume 162 of Progress in Mathematics, pp. 251–261. Birkhäuser, Basel (1996)

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  62. Campillo, A., Gimenez, P.: Graphes arithmetiques et syzygies. Comptes Rendus de l’Académie de Sciences – Série I – Mathématiques 324, 313–316 (1997)

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  63. Campillo, A., Gimenez, P.: Syzygies of affine toric varieties. J. Algebra 225(1), 142–161 (2000)

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  64. Campillo, A., et al.: A Hoschschild homology criterium for the smoothness of an algebra. Commentarii Mathematici Helvetici 69, 163–168 (1994). The following people participated in the research of this paper under the acronym BACH (The Buenos Aires Cyclic Homology Group): Antonio Campillo, Jorge Alberto Guccione, Juan José Guccione, Maria Julia Redondo, Andrea Solotar and Orlando E. Villamayor

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  65. Campillo, A., Olivares, J.: Plane foliations of degree different from one are determined by their singular scheme. Comptes Rendus de l’Académie de Sciences – Série I – Mathématiques 328, 877–882 (1999)

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  66. Campillo, A., Olivares, J.: Assigned conditions and geometry of foliations on the projective plane. In: Brasselet, J.-P., Suwa, T. (eds.) Singularities in Geometry and Topology 1998, Sapporo. Advanced Studies in Pure Mathematics, vol. 29, pp. 97–113. Mathematical Society of Japan, Amsterdam/Tokyo (2000)

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  67. Campillo, A., Olivares, J.: Polarity with respect to a foliation and Caylay-Bacharach theorems. Journal für die reine und angewandte Mathematik 534, 95–118 (2001)

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  68. Campillo, A., Olivares, J.: On sections with isolated singualarities of twisted bundles and applications to foliations by curves. Math. Res. Lett. 10(5–5), 651–658 (2003)

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  69. Campillo, A., Olivares, J.: On the polar linear system of a foliation by curves on the projective spaces. In: Muñoz-Porras, J.M., et al. (eds.) The Geometry of Riemann Surfaces and Abelian Varieties. Volume 397 of Contemporary Mathematics, pp. 7–14. American Mathematical Society (2006). Proceedings of the “III Iberoamerican Congress on Geometry”, in honor of Professor Sevín Recillas-Pishmish’s 60th birthday, Salamanca, Spain, 8–12 June 2004

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  70. Campillo, A., Olivares, J.: Special subschemes of the scheme of singularities of a plane foliation. Comptes Rendus de l’Académie de Sciences – Série I – Mathématiques 344(9), 581–585 (2007)

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  71. Campillo, A., Encinas, S.: Constructing nodes for two variable polynomial interpolation. ACM SIGSAM Bull. 35(4), 17 (2001)

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  72. Campillo, A., Encinas, S.: Some applications of two dimensional complete ideals. In: Commutative Algebra (Grenoble/Lyon, 2001). Volume 331 of Contemporary Mathematics, pp. 55–74. American Mathematical Society (2003)

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  73. Campillo, A., Encinas, S.: Heisuke Hironaka. La Gaceta de la RSME 13(1), 179–190 (2010)

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  74. Campillo, A., Greuel, G.M., Lossen, C.: Equisingular calculations of plane curve singularities. J. Symb. Comput. 42(1–2), 89–114 (2007)

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  75. Campillo, A., Greuel, G.M., Lossen, C.: Equisingular deformations of plane curves in arbitrary characteristic. Compositio Mathematica 143, 829–882 (2007)

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  76. Campillo, A., Fitzpatrick, P., Martínez-Moro, E., Pellikaan, R. (eds.): Special issue algebraic coding theory and applications. J. Symb. Comput. 45(7), 721–824 (2010). From the editors Preface: This issue of the Journal of Symbolic Computation is a follow-up to the “Soria Summer School on Computational Mathematics: Algebraic Coding Theory” supported by the group SINGACOM of the University of Valladolid, held at the Campus Duques de Soria of the University of Valladolid in Soria, 2–11 July 2008 and the Special Session “Computer Algebra and Coding Theory 2008”, hosted at ACA 2008 held at the RISC Institute of the Johannes Kepler University in Hagenberg, Austria, 27–30 July 2008

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  77. Campillo, A., Cardona, G., Melle-Hernández, A., Veys, W., Zúñiga-Galindo, W.A. (eds.): Zeta Functions in Algebra and Geometry. Contemporary Mathematics. American Mathematical Society (2010). The volume contains the proceedings of the “Second International Workshop on Zeta Functions in Algebra and Geometry” held 3–7 May 2010 at the Universitat de les Illes Balears, Palma de Mallorca, Spain

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  78. Campillo, A., Kulhmann, F.V., Teissier, B. (eds.): Valuation Theory in Interaction. EMS Series of Congress Reports. EMS Publishing House, Zürich (2014)

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  79. Campillo, A., Castellanos, J.: Curve Singularities. An Algebraic and Geometric Approach. Actualités Mathématiques, 126pp. Hermann, Paris (2005)

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  82. Campillo, A., Castellanos, J.: On Puiseux exponents for higher dimensional singularities. In: Topics in Algebraic and Noncommutative Geometry. Volume 324 of Contemporary Mathematics, pp. 91–102. American Mathematical Society, Providence (2003)

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  83. Campillo, A.: Hamburger-Noether expansions over rings. Trans. AMS 279(1), 277–388 (1983)

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  84. Campillo, A.: Arithmetical aspects of saturation of singularities. Pol. Acad. Publ. 20, 121–137 (1988)

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Acknowledgements

Among the materials that we have had during the preparation of this paper, we are most grateful for a draft of notes by Antonio Campillo on his mathematical contributions at a much higher resolution than what we have been able to include in this work (the latest version of his notes has over 50 pages). It is like the transcription of music that a composer hears in his mind. We see it as a precise and precious mental map, with all the relevant concepts and connections in place, a generous tour-de-force on his part that will have positive and substantial repercussions in the investigation of the problems raised for many years. Our quotations from it are identified by the initials AC.

We also thank the students and collaborators of Antonio Campillo for providing us with all the answers to our questions and thus facilitating our task of improving and validating the informations in this work. With the understanding, of course, that only the authors are responsible for errors and misconceptions that may have remained.

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Authors and Affiliations

  1. Department of Applied Mathematics, Universidad Politécnica de Valencia, Valencia, Spain

    Francisco Monserrat

  2. Mathematics Department, Universitat Politècnica de Catalunya, Barcelona, Spain

    Sebastià Xambó-Descamps

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  1. Francisco Monserrat
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  2. Sebastià Xambó-Descamps
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Correspondence to Francisco Monserrat .

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Editors and Affiliations

  1. Fachbereich Mathematik, Universität Kaiserslautern, Kaiserslautern, Germany

    Gert-Martin Greuel

  2. Departamento de Álgebra, Instituto de Matemáticas (IMUS), Universidad de Sevilla, Sevilla, Spain

    Luis Narváez Macarro

  3. Departament de Matemàtiques, Universitat Politècnica de Catalunya, Barcelona, Spain

    Sebastià Xambó-Descamps

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Monserrat, F., Xambó-Descamps, S. (2018). Antonio Campillo. In: Greuel, GM., Narváez Macarro, L., Xambó-Descamps, S. (eds) Singularities, Algebraic Geometry, Commutative Algebra, and Related Topics. Springer, Cham. https://doi.org/10.1007/978-3-319-96827-8_1

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