On the total order of reducibility of a pencil of algebraic plane curves

Autor: Guillaume Chèze, Laurent Busé
Přispěvatelé: Geometry, algebra, algorithms (GALAAD), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Toulouse UMR5219 (IMT), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)
Rok vydání: 2011
Předmět:
FOS: Computer and information sciences
Computer Science - Symbolic Computation
Spectrum of a rational function
Plane curve
[MATH.MATH-AC]Mathematics [math]/Commutative Algebra [math.AC]
Physics::Medical Physics
010103 numerical & computational mathematics
Symbolic Computation (cs.SC)
Commutative Algebra (math.AC)
01 natural sciences
Combinatorics
Mathematics - Algebraic Geometry
Mathematics::Algebraic Geometry
Algebraic surface
FOS: Mathematics
Real algebraic geometry
0101 mathematics
Algebraic Geometry (math.AG)
Mathematics::Symplectic Geometry
ComputingMilieux_MISCELLANEOUS
Pencil (mathematics)
Mathematics
Pencil of algebraic curves
[INFO.INFO-SC]Computer Science [cs]/Symbolic Computation [cs.SC]
Circular algebraic curve
Algebra and Number Theory
Butterfly curve (algebraic)
010102 general mathematics
Mathematics - Commutative Algebra
Newtonʼs polygon
Family of curves
Algebraic de Rhamʼs cohomology
[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]
Algebraic curve
Zdroj: Journal of Algebra
Journal of Algebra, Elsevier, 2011, 341 (1), pp.256-278. ⟨10.1016/j.jalgebra.2011.06.006⟩
Journal of Algebra, 2011, 341 (1), pp.256-278. ⟨10.1016/j.jalgebra.2011.06.006⟩
ISSN: 0021-8693
1090-266X
DOI: 10.1016/j.jalgebra.2011.06.006
Popis: International audience; In this paper, the problem of bounding the number of reducible curves in a pencil of algebraic plane curves is addressed. Unlike most of the previous related works, each reducible curve of the pencil is here counted with its appropriate multiplicity. It is proved that this number of reducible curves, counted with multiplicity, is bounded by d^2-1 where d is the degree of the pencil. Then, a sharper bound is given by taking into account the Newton's polygon of the pencil.
Databáze: OpenAIRE
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