Artículo

Botbol, N.; Busé, L.; Chardin, M.; Hassanzadeh, S.H.; Simis, A.; Tran, Q.H."Effective criteria for bigraded birational maps" (2017) Journal of Symbolic Computation. 81:69-87
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Abstract:

In this paper, we consider rational maps whose source is a product of two subvarieties, each one being embedded in a projective space. Our main objective is to investigate birationality criteria for such maps. First, a general criterion is given in terms of the rank of a couple of matrices that became to be known as Jacobian dual matrices. Then, we focus on rational maps from P1×P1 to P2 in very low bidegrees and provide new matrix-based birationality criteria by analyzing the syzygies of the defining equations of the map, in particular by looking at the dimension of certain bigraded parts of the syzygy module. Finally, applications of our results to the context of geometric modeling are discussed at the end of the paper. © 2016 Elsevier Ltd

Registro:

Documento: Artículo
Título:Effective criteria for bigraded birational maps
Autor:Botbol, N.; Busé, L.; Chardin, M.; Hassanzadeh, S.H.; Simis, A.; Tran, Q.H.
Filiación:Departamento de Matemática, FCEN, Universidad de Buenos Aires, Argentina
Université Côte d'Azur, Inria, 2004 route des Lucioles, Sophia Antipolis, 06902, France
Institut de Mathématiques de Jussieu, UPMC, 4 place Jussieu, Paris, 75005, France
Instituto de Matematica, Universidade Federal do Rio de Janeiro, Brazil
Departamento de Matemática, Universidade Federal de Pernambuco, Recife, Pernambuco 50740-560, Brazil
Hue University's College of Education, 34 Le Loi St., Hue City, Viet Nam
Palabras clave:Bigraded base ideal; Bigraded rational maps; Birationality criteria; Jacobian dual rank; Rees algebras
Año:2017
Volumen:81
Página de inicio:69
Página de fin:87
DOI: http://dx.doi.org/10.1016/j.jsc.2016.12.001
Handle:http://hdl.handle.net/20.500.12110/paper_07477171_v81_n_p69_Botbol
Título revista:Journal of Symbolic Computation
Título revista abreviado:J. Symb. Comput.
ISSN:07477171
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_07477171_v81_n_p69_Botbol

Referencias:

  • Botbol, N., The implicit equation of a multigraded hypersurface (2011) J. Algebra, 348, pp. 381-401
  • Bruns, W., Herzog, J., Cohen–Macaulay Rings (1993) Cambridge Studies in Advanced Mathematics, 39. , Cambridge University Press Cambridge
  • Doria, A.V., Hassanzadeh, S.H., Simis, A., A characteristic-free criterion of birationality (2012) Adv. Math., 230 (1), pp. 390-413
  • Eisenbud, D., Commutative Algebra (1995) Graduate Texts in Mathematics, 150. , Springer-Verlag New York With a view toward algebraic geometry
  • Eisenbud, D., Ulrich, B., Row ideals and fibers of morphisms (2008) Mich. Math. J., 57, pp. 261-268
  • Grayson, D.R., Stillman, M.E., Macaulay2, a software system for research in algebraic geometry (2002), http://www.math.uiuc.edu/Macaulay2/, Available at; Hassanzadeh, S.H., Simis, A., Plane Cremona maps: saturation and regularity of the base ideal (2012) J. Algebra, 371, pp. 620-652
  • Russo, F., Simis, A., On birational maps and Jacobian matrices (2001) Compos. Math., 126 (3), pp. 335-358
  • Schost, É., Spaenlehauer, P.-J., A quadratically convergent algorithm for structured low-rank approximation (2015) Found. Comput. Math., pp. 1-36
  • Schreyer, F.-O., Hulek, K., Katz, S., Cremona transformations and syzygies (1992) Math. Z., 209 (3), pp. 419-444
  • Sederberg, T.W., Zheng, J., Birational quadrilateral maps (2015) Comput. Aided Geom. Des., 32, pp. 1-4
  • Simis, A., Cremona transformations and some related algebras (2004) J. Algebra, 280 (1), pp. 162-179
  • Simis, A., Ulrich, B., Vasconcelos, W.V., Rees algebras of modules (2003) Proc. Lond. Math. Soc. (3), 87 (3), pp. 610-646

Citas:

---------- APA ----------
Botbol, N., Busé, L., Chardin, M., Hassanzadeh, S.H., Simis, A. & Tran, Q.H. (2017) . Effective criteria for bigraded birational maps. Journal of Symbolic Computation, 81, 69-87.
http://dx.doi.org/10.1016/j.jsc.2016.12.001
---------- CHICAGO ----------
Botbol, N., Busé, L., Chardin, M., Hassanzadeh, S.H., Simis, A., Tran, Q.H. "Effective criteria for bigraded birational maps" . Journal of Symbolic Computation 81 (2017) : 69-87.
http://dx.doi.org/10.1016/j.jsc.2016.12.001
---------- MLA ----------
Botbol, N., Busé, L., Chardin, M., Hassanzadeh, S.H., Simis, A., Tran, Q.H. "Effective criteria for bigraded birational maps" . Journal of Symbolic Computation, vol. 81, 2017, pp. 69-87.
http://dx.doi.org/10.1016/j.jsc.2016.12.001
---------- VANCOUVER ----------
Botbol, N., Busé, L., Chardin, M., Hassanzadeh, S.H., Simis, A., Tran, Q.H. Effective criteria for bigraded birational maps. J. Symb. Comput. 2017;81:69-87.
http://dx.doi.org/10.1016/j.jsc.2016.12.001