foto(08-2009)

Ignacio Ojeda Martínez de Castilla 

Departamento de Matemáticas
Facultad de Ciencias
Universidad de Extremadura
Avenida de Elvas, s/n
06071-Badajoz (ESPAÑA)

Tlf. (+34) 924 289300 ext 86824
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Grupo GADAC
Grupo SINGACOM

WAG2017

Research

Lead researcher of the group GADAC
Researcher of the Project MTM2012-36917-C03-01 lead by Prof. Felix Delgado (IMUVA).
 
Research interests: Combinatorial aspects of Commutative Algebra. Computational Commutative Algebra. Algebraic Geometry.

Publications listed in:

Research papers:

  • Bravo, José Luis; Fernández García-Hierro, Manuel; Ojeda, Ignacio; Sánchez Fernández, Fernando; Uniqueness of Limit Cycles for Quadratic Vector Fields (work in progress)
  • Branco, Manuel B.; Ojeda, Ignacio; Rosales, José Carlos; The set of numerical semigroups of a given multiplicity and Frobenius number (submitted)
  • García-Sánchez, Pedro A.; Llena, David; Ojeda, Ignacio; Critical binomial ideals of Norhtcott type. arXiv:1705.10268 [math.CA].
  • Ojeda, Ignacio; Vigneron-Tenorio, Alberto; The short resolution of a semigroup algebra. To apper in Bulletin of the Australian Mathematical Society. arXiv:1512.00345 [math.RA].
  • Assi, Abdallah; García-Sánchez, Pedro A.; Ojeda, Ignacio. Frobenius vectors, Hilbert series and gluings . arXiv:1311.1988 [math.AC]. Journal of Commutative Algebra, 7 (2015), no. 3, 317-335.
  • Márquez-Campos, Guadalupe; Ojeda, Ignacio; Tornero, José M.; On the computation of the Apéry set of numerical monoids and affine semigroups. Semigroup Forum 91 (2015), no. 1, 139-158.
  • Ojeda, Ignacio. Kronecker Square Roots and The Block vec Matrix. Amer. Math. Monthly 121 (2015), no. 1, 60-64. arXiv:1310.8149 [math.GM]
  • Katsabekis, Anargyros; Ojeda, Ignacio. An indispensable classification of monomial curves in A^4(k). Pacific J. Math. 268 (2014), no. 1, 96-116. arXiv:1103.4702[math.AC]
  • Garcia-Sanchez, Pedro A.; Ojeda, Ignacio; Sanchez-R.-Navarro, Alfredo. Factorization invariants in half-factorial affine semigroups. Int. J. Algebra Comput. 23, 111 (2013) arXiv:1207.5838 [math.AC]
  • Garcia-Sanchez, Pedro A.; Ojeda, Ignacio; Rosales, José Carlos. Affine semigroups having a unique Betti element. J. Algebra Appl. 12, 1250177 (2013) [11 pages] arXiv:1203.4138 [math.AC]
  • Ojeda, Ignacio. Binomial canonical decomposition of binomial ideals. Communications in Algebra, 39 (2011), no. 10, 3722-3735. arXiv:1003.1701[math.AC]
  • Garcia-Sanchez, Pedro A.; Ojeda, Ignacio. Uniquely presented finitely generated commutative monoids. Pacific J. Math. 248 (2010), no. 1, 91-105. arXiv:0907.4241[math.AC]
  • Ojeda, Ignacio; Vigneron-Tenorio, A. Indispensable binomials in semigroup ideals . Proc. Amer. Math. Soc. 138 (2010), 4205-4216. arXiv:0903.1030[math.AC]
  • Notari, Roberto; Ojeda, Ignacio; Spreafico, Maria Luisa. Doubling rational normal curves. Alonso, María Emilia (ed.) et al., Liaison, Schottky problem and invariant theory. Remembering Federico Gaeta. Basel: Birkhauser. Progress in Mathematics 280, 149-187 (2010).arXiv:0812.2578[math.AG]
  • Ojeda, Ignacio; Vigneron-Tenorio, A. Simplicial complexes and minimal free resolution of monomial algebras. J. Pure Appl. Algebra 214 (2010), no. 6, 850-861.arXiv:0810.4836[math.AC]
  • Ojeda Martínez de Castilla, Ignacio. Examples of generic lattice ideals of codimension 3. Comm. Algebra 36 (2008), no. 1, 279-287.
  • Notari, R.; Ojeda, I. Even $G$-liaison classes of some unions of curves. J. Pure Appl. Algebra 204 (2006), no. 2, 389-412.
  • Notari, Roberto; Ojeda, Ignacio; Spreafico, Maria Luisa. Non degenerate projective curves with very degenerate hyperplane section. Math. Z. 251 (2005), no. 2, 443-473.
  • Ojeda Martínez de Castilla, Ignacio; Pisón Casares, Pilar. On the hull resolution of an affine monomial curve. J. Pure Appl. Algebra 192 (2004), no. 1-3, 53-67.
  • Ojeda Martínez de Castilla, Ignacio; Piedra Sánchez, Ramón. Index of nilpotency of binomial ideals. J. Algebra 255 (2002), no. 1, 135-147.
  • Ojeda Martínez de Castilla, Ignacio; Sánchez, Ramón Peidra. Cellular binomial ideals. Primary decomposition of binomial ideals. J. Symbolic Comput. 30 (2000), no. 4, 383-400.
  • Other publications:

    1. Ph. D Thesis. Ideales Binomiales y Aplicaciones (Spanish), Universidad de Sevilla 2000.
    2. Ojeda Martínez de Castilla, Ignacio; Piedra Sánchez, Ramón Pilar Pisón Casares, in memoriam. (Spanish) Gac. R. Soc. Mat. Esp. 10 (2007), no. 3, 637-642.
    3. Book of abstracts. II Iberian Mathematical Meeting (I. Ojeda, ed.) ISBN: 978-84-692-3591-1.

    Software:

    1. apery.lib, Singular library for the computation of the apery set and the frobenius number of a numerical semigroup (2015).
    2. binomialCD.m2, Macaulay2 package for a cellular decomposition (1999). This package has been improved by T. Kahle and included in Kahle's Macaulay2 package binomial.m2

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