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Publications

All my published papers, preprints and lecture notes are available in the open archive HAL:

List of publications, sorted by year of publication, with DOI and links to preprint versions

Below, my publications are sorted first by research themes, then by year of publication.

Recent preprints

  • Matías Bender, Laurent Busé, Carles Checa and Elias Tsigaridas. Multigraded Castelnuovo-Mumford regularity and Gröbner bases (preprint).

  • Matías Bender, Laurent Busé, Carles Checa and Elias Tsigaridas. Solving bihomogeneous polynomial systems with a zero-dimensional projection (preprint).

Elimination theory, resultants and discriminants

  • Laurent Busé, Carles Checa. Toric Sylvester forms. Journal of Pure and Applied Algebra, to appear, 228(11):107739, 2024. (preprint).

  • Laurent Busé. Formulas for the eigendiscriminants of ternary and quaternary forms. Linear and Multilinear Algebra, 71(11):1755-1774, 2023 (preprint).

  • Laurent Busé, Marc Chardin and Navid Nemati. Multigraded Sylvester forms, duality and elimination matrices. Journal of Algebra, 609(1):514-546, 2022 (preprint, talk at MCA21).

  • 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 and Pablo Mazón. Construction of birational trilinear volumes via tensor rank criteria. SIAM Journal on Applied Algebra and Geometry, to appear (preprint).

  • Laurent Busé, Pablo Gonzáles-Mazón and Josef Schicho. Trilinear birational maps in dimension three. Mathematics of Computations, 92:1837-1866, 2023 (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, Katia Turcot, Raphaël Zory. Improved markerless gait kinematics measurement using a biomechanically-aware algorithm with subject-specific geometric modeling. Measurement, 234:114857, 2024 (preprint).

  • Tong Zhao, Laurent Busé, David Cohen-Steiner, Tamy Boubekeur, Jean-Marc Thiery, Pierre Alliez. Variational Shape Reconstruction via Quadric Error Metrics. ACM Transactions on Graphics (SIGGRAPH) 2023, Art. 45:1-10, 2023 (preprint).

  • 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, 145:111358, 2022 (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).

Book

  • Laurent Busé, Fabrizio Catanese and Elisa Postinghel. Algebraic Curves and Surfaces, A History of Shapes. SISSA Springer Series, vol 4. Springer, 2023 (DOI).

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

  • Editor for the Journal of Pure and Applied Algebra (see also this page) since September 2023.

  • 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).