All my published papers, unpublished notes or lecture notes are available on the HAL preprint server.

See also my  profile in
Google Scholar.

Preprints:

  • Busé, Laurent; Dimca, Alexandru; Sticlaru, Gabriel; Freeness and invariants of rational plane curves (preprint).
  • Busé, Laurent; Mantzaflaris, Angelos; Tsigaridas, Elias; Matrix formulae for resultants and discriminants of bivariate tensor-product polynomials (preprint). 

Published papers organised by topics:

Syzygies and the geometry of rational maps

  • Botbol, Nicolas; Busé, Laurent; Chardin, Marc; Hassanzadeh, Hamid; Simis, Aron; Tran, Quang Hoa. Effective criteria for bigraded birational maps.
    Journal of Symbolic Computation, 81 (2017), 69-87 (preprint).
  • Botbol, Nicolas; Busé, Laurent; Chardin, Marc. Fitting ideals and multiple-points of surface parameterizations.
    Journal of Algebra, 
     420 (2014), 486-508 (preprint). 
    (Accepted for presentation at the MEGA2013 international conference). 
  • Busé, Laurent; Chardin, Marc; Simis, Aron. Elimination and nonlinear equations of Rees Algebras, with an appendix by J. Oesterlé.
    Journal of Algebra324 (2010) vol. 6, 1314-1333 (preprint).
  • Busé, Laurent; Chardin, Marc; Jouanolou, Jean-Pierre. Torsion of the symmetric algebra and implicitization.
    Proceedings of the American Mathematical Society137 (2009) vol. 6, 1855-1865 (preprint).
  • Busé, Laurent; Dohm, Marc. Implicitization of Bihomogeneous Parametrizations of Algebraic Surfaces via Linear Syzygies.
    ACM proceedings of the international conference on Symbolic and Algebraic Computation (ISSAC), (2007), 69-76 (preprint).
    (
    Best student paper award for Marc Dohm).
  • Busé, Laurent; D’Andrea, Carlos. A matrix-based approach to properness and inversion problems for rational surfaces. 
    Applicable Algebra in Engineering, Communication and Computing17 (2006) vol. 6, 393-407 (preprint).
  • Busé, Laurent; Chardin, Marc. Implicitizing rational hypersurfaces using approximation complexes.
    Journal of Symbolic Computation40 (2005) vol. 4-5, 1150-1168 (preprint).
  • Busé, Laurent; Jouanolou, Jean-Pierre. On the closed image of a rational map and the implicitization problem.
    Journal of Algebra265 (2003) vol. 1, 312-357 (preprint).
  • Busé, Laurent; Cox, David; D’Andrea, Carlos. Implicitization of surfaces in the projective space in the presence of base points. 
    Journal of Algebra and Its Applications2 (2003) vol. 2, 189-214 (preprint).

Algebraic methods for geometric modeling

  • Busé, Laurent; Galligo, André; Extraction of Tori from minimal point sets.
    Computer Aided Geometric Design, 58 (2017), 1-7 (preprint). 
  • Busé, Laurent; Galligo, André; Zhang, Jiajun. Extraction of cylinders and cones from minimal point sets.
    Graphical Models, 86 (2016), 1-12 (preprint).
  • Shen, Jingjing; Busé, Laurent; Alliez, Pierre; Dodgson, Neil. A line/trimmed NURBS surface intersection algorithm using matrix representations.
    Computer Aided Geometric Design, 48 (2016), 1-16 (preprint). 
  • Busé, Laurent. Implicit matrix representations of rational Bézier curves and surfaces.
    Computer Aided Design46 (2014), 14-24, 
    2013 SIAM Conference on Geometric and Physical Modeling (preprint).
    (Best paper award, 1st place) 
  • Busé, Laurent. Intersection entre courbes et surfaces rationnelles au moyen des représentations implicites matricielles. 
    Revue Electronique Francophone d'Informatique Graphique (REFIG)6 (2012) vol. 1, 27-37 (preprint).
  • Busé, Laurent; Thang Luu Ba. The surface/surface intersection problem by means of matrix based representations. 
    Computer Aided Geometric Design29 (2012), vol. 8, 579-598 (preprint).
  • Busé, Laurent; Luu Ba, Thang. Matrix-based implicit representations of rational algebraic curves and applications. 
    Computer Aided Geometric Design27 (2010) vol. 9, 681-699 (preprint).
  • Busé, Laurent; Elkadi Mohamed; Galligo, André. A computational study of rational ruled surfaces.
    Journal of Symbolic Computation44 (2009) vol. 3, 232-241 (preprint).
  • Luu Ba, Thang; Busé, Laurent; Mourrain, Bernard. Curve/surface intersection problem by means of matrix representations.
    ACM proceedings of the international conference on Symbolic and Numerical Computation (SNC), (2009), 71-78 (preprint).
  • Busé, Laurent; Goldman, Ron. Division Algorithms for Bernstein Polynomials.
    Computer Aided Geometric Design25 (2008) vol. 9, 850-865 (preprint).
  • Busé, Laurent; D’Andrea, Carlos. Inversion of parameterized hypersurfaces by means of subresultants.
    ACM proceedings of the international Symposium on Symbolic and Algebraic Computing (ISSAC),  (2004), 65-71 (
    preprint).
  • Busé, Laurent; Galligo, André. Using semi-implicit representation of algebraic surfaces.
    Proceedings of the international conference Shape Modeling and Applications (SMI), (2004), 342-345 (preprint).

Singularities and discriminants of polynomial equations

  • Busé, Laurent; Nonkané, Ibrahim. Discriminants of complete intersection space curves.
    ACM proceedings of the International Symposium on Symbolic and Algebraic Computation (ISSAC), (2017), 69-76  (preprint)
  • Busé, Laurent; Jouanolou, Jean-Pierre. On the discriminant scheme of homogeneous polynomials.
    Mathematics in Computer Science(2014), vol. 2, 175-234 (preprint).
    (Special Issue on Computational Algebraic Geometry. Guest Editors : Sandra Di Rocco, Josef Schicho).
  • Busé, Laurent; D’Andrea, Carlos. Singular factors of rational plane curves. 
    Journal of Algebra357 (2012), 322-346 (preprint).
  • Busé, Laurent; Chèze, Guillaume. On the total order of reducibility of a pencil of algebraic plane curves. 
    Journal of Algebra341 (2011) vol. 1, 256-278 (preprint).
  • Busé, Laurent; Chèze, Guillaume; Najib, Salah. Noether's forms for the study of non-composite rational functions and their spectrum.
    Acta Arithmetica, 147 (2011) vol. 3, 217-231 (preprint).
  • Busé, Laurent. On the equations of the moving curve ideal.
    Journal of Algebra321 (2009) vol. 8, 2317-2344 (preprint).
  • Busé, Laurent; Mourrain, Bernard. Explicit factors of some iterated resultants and discriminants.
    Mathematics of Computations78 (2009) vol. 265, 345-386 (preprint).

Resultants and solving of structured polynomial systems

  • Busé, Laurent; Karasoulou, Anna. Resultant of an equivariant polynomial system with respect to the symmetric group.
    Journal of Symbolic Computation76 (2016), 142-157 (preprint).
  • Busé, Laurent; Elkadi Mohamed; Galligo, André. Intersection and self-intersection of surfaces by means of Bezoutian matrices.
    Computer Aided Geometric Design25 (2008) vol. 2, 53-68 (preprint).
  • Busé, Laurent; Galligo, André. Semi-implicit representations of surfaces in the projective space, resultants and applications. 
    Journal of Symbolic Computation39 (2005) vol. 3-4, 317-329 (preprint).
  • Busé, Laurent; Khalil, Houssam; Mourrain, Bernard. Resultant-based methods for plane curves intersection problems. 
    Proceedings of the international conference on Computer Algebra in Scientific Computing (CASC), Lecture Notes in Computer Sciences, 3718 (2005), 75-92 (preprint).
  • Busé, Laurent. Resultants of determinantal varieties. 
    Journal of Pure and Applied Algebra193 (2004) vol. 1-3, 71-97 (preprint).
  • Busé, Laurent; D’Andrea, Carlos. On the irreducibility of multivariate subresultants.
    Comptes-Rendus de l'Académie des Sciences, Série 1, Mathématiques338 (2004) vol. 4, 287-290 (preprint).
  • Busé, Laurent; Galligo, André. A resultant approach to detect intersecting curves in the projective space.
    Proceedings of the international conference on Methods in Effective Algebraic Geometry (MEGA),  (2003), electronic (preprint).
  • Busé, Laurent, Elkadi, Mohamed, Mourrain, Bernard. Using projection operators in computer aided geometric design.
    Comtemporary Mathematics334 (2003) 321-342 (preprint).
  • Busé, Laurent; Elkadi, Mohamed; Mourrain, Bernard. Resultant over the residual of a complete intersection.
    Journal of Pure and Applied Algebra164 (2001) vol. 1-2, 35-57 (preprint).
  • Busé, Laurent. Residual resultant over the projective plane and the implicitization problem.
    ACM proceedings of the international conference International Symposium on Symbolic and Algebraic Computing (ISSAC), (2001) 48-55  (preprint)
    (
    Best student paper award).
  • Busé, Laurent; Elkadi, Mohamed; Mourrain, Bernard. Generalized resultants over unirational algebraic varieties.
    Journal of Symbolic Computation 29 (2000) vol. 4-5, 515-526 (preprint).

Theses :

  • Busé, Laurent. Représentations matricielles en théorie de l'élimination et applications à la géométrie.
    Habilitation à Diriger des Recherches, university of Nice, april 29, 2011 (preprint).
  • Busé, Laurent. Étude du résultant sur une variété algébrique.
    PhD thesis, university of Nice, december 19, 2001 (preprint).

Book chapter :

  • Hahman, S.: Belyaev, A.; Busé, L.; Elber, G.; Mourrain, B.; Roessl, C. Shape Interrogation.  
    Shape Analysis and Structuring, Mathematics and Visualization, Springer, (2007) 57 pages (preprint).

Book edited :

  • Busé, Laurent; Elkadi, Mohamed; Mourrain, Bernard. Computational Algebraic Geometry and Applications.
    Theoretical Computer Science 392 (2008) vol. 1-3, 1-178 (preprint).
    (In honor of the 60th birthday of André Galligo).

Lecture notes :

  • "Résultant univarié et courbes algébriques planes", (2006-2008) 38 pages. Notes in french of lectures given at the Master of mathematics, 2nd year, of the University of Nice (preprint)
  • "Elimination theory in codimension one and applications", INRIA research report 5918, (2006) 47 pages. Notes of lectures given at the CIMPA-UNESCO-IRAN school in Zanjan, Iran, July 9-22 2005 (preprint)
  • "Géométrie différentielle et applications", (2004) 25 pages. Notes of lectures on differential geometry given at the university of Nice (preprint)
  • "Syzygies of points in a projective space", with H-C. Von Bothmer and B. Fu, (2002) 28 pages. These notes are collected from talks given by the authors at the University of Nice (october-december 2002) (preprint)

Others :

  • Busé, Laurent. Computing resultant matrices with Macaulay2 and Maple. 
    INRIA Technical Report 280 (2003), pp. 33 (preprint).


Slides of some selected talks about my work :