Fibers of rational maps and Rees algebras of their base ideals
Vol. 129 No. 1B (2020), Original Article
Vol. 129 No. 1B (2020)

Fibers of rational maps and Rees algebras of their base ideals

Original Article
https://doi.org/10.26459/hueuni-jns.v129i1B.5349
Published 2020-06-22
Tran Quang Hoa
University of Education, Hue University, 34 Le Loi St., Hue, Vietnam
Ho Vu Ngoc Phuong
University of Sciences, Hue University, 77 Nguyen Hue St., Hue, Vietnam
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Keywords

approximation complexes
base ideals
fibers of rational maps
parameterizations
Rees algebras

How to Cite

1.
Hoa TQ, Ngoc Phuong HV. Fibers of rational maps and Rees algebras of their base ideals. hueuni-jns [Internet]. 2020Jun.22 [cited 2024Nov.15];129(1B):5-14. Available from: http://222.255.146.83/index.php/hujos-ns/article/view/5349
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Abstract

We consider a ratinonal map $\phi$ from m-dimensional projective space to n-dimensional projective space that is a parameterization of m-dimensional variety. Our main goal is to study the (m-1)-dimensional fibers of $\phi$ in relation with the m-th local cohomology modules of Rees algebra of its base ideal.
https://doi.org/10.26459/hueuni-jns.v129i1B.5349
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References

  1. Cox D. What is the role of algebra in applied mathematics?. Notices of the AMS.2005;52(10):1193-1198.
  2. Chardin M, Cutkosky SD, Tran QH. Fibers of rational maps and jacobian matrices. Journal of Algebra. 2019.
  3. Tran QH. Bound for the number of one-dimensional fibers of a projective morphism. Journal of Algebra. 2018;494:220-236.
  4. Botbol N, Busé L, Chardin M. Fitting ideals and multiple points of surface parameterizations. Journal of Algebra. 2014;420:486-508.
  5. Zariski O, Samuel P. Commutative algebra, Vol II. Berlin: Springer; 1960.
  6. Daniel G, Michael S, David E. Macaulay2. Version 1.16. Illinois: National Science Foundation; 2020.
  7. Chardin M. Powers of ideals and the cohomology of stalks and fibers of morphisms. Algebra & Number Theory. 2013;7(1):1-18.
  8. Herzog J, Simis A, Vasconcelos W. Approximation complexes of blowing-up rings. Journal of Algebra. 1982;74(2):466-493.
  9. Busé L, Chardin M. Implicitizing rational hypersurfaces using approximation complexes. Journal of Symbolic Computation. 2005;40(4-5): 1150-1168.
  10. Chardin M, Fall AL, Nagel U. Bounds for the Castelnuovo–Mumford regularity of modules. Mathematische Zeitschrift. 2007;258(1):69-80.
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