Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
권호 표지
DOI QR코드

DOI QR Code

SOME GEOMETRIC CONSEQUENCES OBTAINED FROM PARTIAL ELIMINATION IDEALS

  • Ahn, Jeaman (Department of Mathematics Education Kongju National University)
  • Received : 2010.05.09
  • Accepted : 2010.08.30
  • Published : 2010.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

In [9], M. Green introduced the partial elimination ideals defining the multiple loci of the projection image of a closed subscheme in ${\mathbb{P}}^n$. In this paper, we give some geometric consequences obtained from partial elimination ideals.

Keywords

Acknowledgement

Supported by : National Research Foundation of Korea (NRF)

References

  1. J. Ahn, The degree-complexity of the defining ideal of a smooth integral curve. J. Symbolic Comput. 43 (2008), no. 6-7, 422-441. https://doi.org/10.1016/j.jsc.2007.07.008
  2. D. Bayer and D. Mumford, What can be computed in algebraic geometry? Computational algebraic geometry and commutative algebra (Cortona, 1991), 1-48, Sympos. Math., XXXIV, Cambridge Univ. Press, Cambridge, 1993.
  3. D. Cox, J. Little, and D. O'Shea, Ideals, varieties, and algorithms. An introduction to computational algebraic geometry and commutative algebra. Second edition. Undergraduate Texts in Mathematics. Springer-Verlag, New York, 1997.
  4. D. Cox, J. Little, and D. O'Shea, Using algebraic geometry. Graduate Texts in Mathematics, 185. Springer-Verlag, New York, 1998.
  5. A. Conca and J. Sidman, Generic initial ideals of points and curves. J. Symbolic Comput. 40 (2005).
  6. D. Eisenbud, The geometry of syzygies. A second course in commutative algebra and algebraic geometry. Graduate Texts in Mathematics, 229. Springer-Verlag, New York, 2005.
  7. D. Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate Texts in Mathematics, 150. Springer-Verag, New York, 1995.
  8. D. Eisenbud and S. Goto. Linear free resolutions and minimal multiplicity, J. Algebra 88, 1984, 89-133. https://doi.org/10.1016/0021-8693(84)90092-9
  9. M. Green, Generic Initial Ideals, in Six lectures on Commutative Algebra, (Elias J., Giral J.M., Miro-Roig. R.M., Zarzuela S., eds.), Progress in Mathematics 166, Birkhauser, 1998, 119-186.
  10. M. Haiman, Hilbert schemes, polygraphs and the Macdonald positivity conjec- ture, J. Amer. Math. Soc. 14 (2001), 941-1006 https://doi.org/10.1090/S0894-0347-01-00373-3