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Publications

All my published papers, preprints and lecture notes are available in the open archive HAL; you can browse them here, listed by year of publications. Below, they are listed by research topics, with a direct link to the preprint versions.

Recent preprints

  • Laurent Busé, Carles Checa. Toric Sylvester forms and applications in elimination theory (preprint).

Elimination theory, resultants and discriminants

  • Laurent Busé, Marc Chardin and Navid Nemati. Multigraded Sylvester forms, duality and elimination matrices. Journal of Algebra, to appear (preprint, talk at MCA21).

  • Laurent Busé. Formulas for the eigendiscriminants of ternary and quaternary forms. Linear and Multilinear Algebra, to appear (preprint).

  • Laurent Busé and Thomas Dedieu. Generalized weight properties of resultants and discriminants, and applications to projective enumerative geometry. To appear in a collection of notes on Degeneration and enumeration of curves on surfaces by Thomas Dedieu, in preparation (preprint).

  • Laurent Busé, Angelos Mantzaflaris and Elias Tsigaridas. Matrix formulae for resultants and discriminants of bivariate tensor-product polynomials. Journal of Symbolic Computation, 98:65-83, 2020 (preprint).

  • Laurent Busé and Ibrahim Nonkané. Discriminants of complete intersection space curves. ACM proceedings of ISSAC, p. 69-76, 2017 (preprint).

  • Laurent Busé and Anna Karasoulou. Resultant of an equivariant polynomial system with respect to the symmetric group. Journal of Symbolic Computation, 76:142-157, 2016 (preprint).

  • Laurent Busé and Jean-Pierre Jouanolou. On the discriminant scheme of homogeneous polynomials. Mathematics in Computer Science, 8(2):175-234, 2014 (preprint).

  • Laurent Busé. Resultants of determinantal varieties. Journal of Pure and Applied Algebra, 193(1-3):71-97, 2004 (preprint).

  • Laurent Busé and Carlos D’Andrea. On the irreducibility of multivariate subresultants. Comptes-Rendus de l'Académie des Sciences, Série 1, Mathématiques, 338(4):287-290, 2004 (preprint).

  • Laurent Busé, Mohamed Elkadi and Bernard Mourrain. Using projection operators in computer aided geometric design. Comtemporary Mathematics, 334:321-342, 2003 (preprint).

  • Laurent Busé, Mohamed Elkadi and Bernard Mourrain. Resultant over the residual of a complete intersection. Journal of Pure and Applied Algebra, 164(1-2):35-57, 2001 (preprint).

  • Laurent Busé. Residual resultant over the projective plane and the implicitization problem. ACM proceedings of ISSAC, p. 48-55, 2001 (preprint, best student paper award).

  • Laurent Busé, Mohamed Elkadi and Bernard Mourrain. Generalized resultants over unirational algebraic varieties. Journal of Symbolic Computation, 29(4-5):515-526, 2000 (preprint).

Syzygies and the geometry of rational maps

  • Laurent Busé, Pablo Gonzáles-Mazón and Josef Schicho. Trilinear birational maps in dimension three. Mathematics of Computations, to appear (preprint).

  • Laurent Busé and Marc Chardin. Fibers of rational maps and elimination matrices: an application oriented approach. Commutative Algebra - Expository papers dedicated to David Eisenbud on the occasion of his 75th birthday, Springer, Irena Peeva editor, p. 189–217, 2021 (preprint).

  • Laurent Busé and Falai Chen. Determinantal tensor product surfaces and the method of moving quadrics. Transactions of the American Mathematical Society, 374:4931-4952, 2021 (preprint).

  • Nicolás Botbol, Laurent Busé, Marc Chardin and Fatmanur Yildirim. Fibers of multi-graded rational maps and orthogonal projection onto rational surfaces. SIAM Journal on Applied Algebra and Geometry, 4(2):322-353, 2020 (preprint).

  • Laurent Busé, Yairon Cid-Ruiz and Carlos D’Andrea. Degree and birationality of multi-graded rational maps. Proceedings of the London Mathematical Society, 121(4):743-787, 2020 (preprint).

  • Laurent Busé, Clément Laroche and Fatmanur Yildirim. Implicitizing rational curves by the method of moving quadrics. Computer Aided Design (proceedings of SPM conference), 114:101-111, 2019 (preprint).

  • Nicolás Botbol, Laurent Busé, Marc Chardin, Hamid Hassanzadeh, Aron Simis and Quang Hoa Tran. Effective criteria for bigraded birational maps. Journal of Symbolic Computation, 81:69-87, 2017 (preprint).

  • Nicolás Botbol, Laurent Busé and Marc Chardin. Fitting ideals and multiple-points of surface parameterizations. Journal of Algebra, 420:486-508, 2014 (preprint).

  • Laurent Busé, Marc Chardin and Aron Simis. Elimination and nonlinear equations of Rees Algebras, with an appendix by J. Oesterlé. Journal of Algebra, 324(6):1314-1333, 2010 (preprint).

  • Laurent Busé and Thang Luu Ba. Matrix-based implicit representations of rational algebraic curves and applications. Computer Aided Geometric Design, 27(9):681-699, 2010 (preprint).

  • Laurent Busé, Marc Chardin and Jean-Pierre Jouanolou. Torsion of the symmetric algebra and implicitization. Proceedings of the American Mathematical Society, 137(6):1855-1865, 2009 (preprint).

  • Laurent Busé. On the equations of the moving curve ideal. Journal of Algebra, 321(8):2317-2344, 2009 (preprint).

  • Laurent Busé and Ron Goldman. Division Algorithms for Bernstein Polynomials. Computer Aided Geometric Design, 25(9):850-865, 2008 (preprint).

  • Laurent Busé and Marc Dohm. Implicitization of Bihomogeneous Parametrizations of Algebraic Surfaces via Linear Syzygies. ACM proceedings of ISSAC, p. 69-76, 2007 (preprint, best student paper award for Marc Dohm).

  • Laurent Busé and Marc Chardin. Implicitizing rational hypersurfaces using approximation complexes. Journal of Symbolic Computation, 40(4-5):150-1168, 2005 (preprint).

  • Laurent Busé and Jean-Pierre Jouanolou. On the closed image of a rational map and the implicitization problem. Journal of Algebra, 265(1):312-357, 2003 (preprint).

  • Laurent Busé, David Cox and Carlos D’Andrea. Implicitization of surfaces in the projective space in the presence of base points. Journal of Algebra and Its Applications, 2(2):189-214, 2003 (preprint).

Singularities of algebraic curves and surfaces

  • Laurent Busé, Alexandru Dimca, Hal Schenck and Gabriel Sticlaru. The Hessian polynomial and the Jacobian ideal of a reduced hypersurface in P^n. Advances in Mathematics, 392(3):108035, 2021 (preprint).

  • Laurent Busé, Alexandru Dimca and Gabriel Sticlaru. Freeness and invariants of rational plane curves. Mathematics of Computation, 89:1525-1546, 2020 (preprint).

  • Laurent Busé, Carlos D’Andrea, Martin Sombra and Martin Weimann. The geometry of the flex locus of a hypersurface. Pacific Journal of Mathematics, 304(2):419-437, 2020 (preprint).

  • Laurent Busé and Carlos D’Andrea. Singular factors of rational plane curves. Journal of Algebra, 357:322-346, 2012 (preprint).

  • Laurent Busé and Guillaume Chèze. On the total order of reducibility of a pencil of algebraic plane curves. Journal of Algebra, 341(1):256-278, 2011 (preprint).

  • Laurent Busé, Guillaume Chèze and Salah Najib. Noether's forms for the study of non-composite rational functions and their spectrum. Acta Arithmetica, 147(3):217-231, 2011 (preprint).

  • Laurent Busé and Bernard Mourrain. Explicit factors of some iterated resultants and discriminants. Mathematics of Computation, 78(265):345-386 (preprint).

Intersection problems in geometric modeling

  • Xiao, Xiao, Laurent Busé and Fehmi Cirak. A non-iterative method for robustly computing the intersections between a line and a curve or surface. International Journal for Numerical Methods in Engineering, 120:382-390, 2019 (preprint).

  • Laurent Busé. Implicit matrix representations of rational Bézier curves and surfaces. Computer Aided Design (proceedings of 2013 SIAM GD & SPM conferences), 46:14-24, 2014 (preprint, best paper award, 1st place).

  • Laurent Busé. Intersection entre courbes et surfaces rationnelles au moyen des représentations implicites matricielles. Revue Electronique Francophone d'Informatique Graphique (REFIG), 6(1):27-37, 2012 (preprint).

  • Laurent Busé and Thang Luu Ba. The surface/surface intersection problem by means of matrix based representations. Computer Aided Geometric Design, 29(8):579-598, 2012 (preprint).

  • Laurent Busé, Mohamed Elkadi and André Galligo. A computational study of rational ruled surfaces. Journal of Symbolic Computation, 44(3):232-241, 2009 (preprint).

  • Thang Luu Ba, Laurent Busé and Bernard Mourrain. Curve/surface intersection problem by means of matrix representations. ACM proceedings of the international conference on Symbolic and Numerical Computation (SNC), p. 71-78, 2009 (preprint).

  • Laurent Busé, Mohamed Elkadi and André Galligo. Intersection and self-intersection of surfaces by means of Bezoutian matrices. Computer Aided Geometric Design, 25(2):53-68, 2008 (preprint).

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

  • Laurent Busé and Carlos D’Andrea. A matrix-based approach to properness and inversion problems for rational surfaces. Applicable Algebra in Engineering, Communication and Computing, 17(6):393-407, 2006 (preprint).

  • Laurent Busé, Houssam Khalil and Bernard Mourrain. Resultant-based methods for plane curves intersection problems. Lecture Notes in Computer Sciences (proceedings of CASC), 3718:75-92, 2005 (preprint).

  • Laurent Busé and André Galligo. Semi-implicit representations of surfaces in the projective space, resultants and applications. Journal of Symbolic Computation, 39(3-4):317-329, 2005 (preprint).

  • Laurent Busé and Carlos D’Andrea. Inversion of parameterized hypersurfaces by means of subresultants. ACM proceedings of ISSAC, p. 65-71, 2004 (preprint).

  • Laurent Busé and André Galligo. Using semi-implicit representation of algebraic surfaces. Proceedings of the international SMI conference, p. 342-345, 2004 (preprint).

  • Laurent Busé and André Galligo. A resultant approach to detect intersecting curves in the projective space. Proceedings of the MEGA conference, electronic, 2003 (preprint).

Algebraic representations and methods in 3D geometry processing

  • Mehran Hatamzadeh, Laurent Busé, Frédéric Chorin, Pierre Alliez, Jean-Dominique Favreau, Raphaël Zory. A kinematic-geometric model based on ankles’ depth trajectory in frontal plane for gait analysis using a single RGB-D camera. Journal of Biomechanics, to appear (preprint).

  • Xiao, Xiao, Pierre Alliez, Laurent Busé and Laurent Rineau. Delaunay meshing and repairing of NURBS models. Computer Graphics Forum (proceedings of SGP 2021), 40:125-142, 2021 (preprint).

  • Thong Zhao, Pierre Alliez, Tamy Boubekeur and Jean-Marc Thiery. Progressive discrete domains for implicit surface reconstruction. Computer Graphics Forum (proceedings of SGP 2021), 40:143-156, 2021 (preprint).

  • Leman Feng, Pierre Alliez, Laurent Busé, Hervé Delingette and Mathieu Desbrun. Curved optimal Delaunay triangulation. ACM Transactions on Graphics (SIGGRAPH), 37(4), Art. 61, 2018 (preprint).

  • Laurent Busé and André Galligo. Extraction of Tori from minimal point sets. Computer Aided Geometric Design, 58:1-7, 2017 (preprint).

  • Laurent Busé, André Galligo and Jiajun Zhang. Extraction of cylinders and cones from minimal point sets. Graphical Models, 86:1-12, 2016 (preprint).

  • Jingjing Shen, Laurent Busé, Pierre Alliez and Neil Dodgson. A line/trimmed NURBS surface intersection algorithm using matrix representations. Computer Aided Geometric Design, 48:1-16, 2016 (preprint).

Theses

  • Laurent Busé. Représentations matricielles en théorie de l'élimination et applications à la géométrie. Habilitation à Diriger des Recherches, University of Nice, April 29, 2011 (preprint).

  • Laurent Busé. Étude du résultant sur une variété algébrique. PhD thesis, University of Nice, December 19, 2001 (preprint).

Editorial activities

  • Member of the editorial team of Maple Transactions since May 2021.

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

Lecture notes

  • Computational Algebraic Geometry, 2020-2022, 90 pages. Notes of lectures given at the Master of mathematics, 2nd year, of the University Côte d'Azur (preprint).

  • 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).