Fibers of rational maps and Rees algebras of their base ideals

Authors

  • Hoa Tran Quang
  • Ngoc Phuong Ho Vu

Keywords

approximation complexes, base ideals, fibers of rational maps, parameterizations, Rees algebras

DOI:

https://doi.org/10.26459/hueuni-jns.v129i1B.5349

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.

Downloads

Download data is not yet available.

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.

Downloads

Published

2020-06-22

Issue

Section

Original Article