Fibers of rational maps and Rees algebras of their base ideals


approximation complexes
base ideals
fibers of rational maps
Rees algebras

How to Cite

Hoa TQ, Ngoc Phuong HV. Fibers of rational maps and Rees algebras of their base ideals. HueUni-JNS [Internet]. 2020Jun.22 [cited 2020Oct.1];129(1B):5-14. Available from:


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.


  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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