Abstract
P^n’de bir projektif variyeti W ve bu variyetinin üzerinde olmayan bir p noktası alalım. p noktasından P^(n-1) 'e bir izdüşüm π_p:P^n\{p}→P^(n-1) fonksiyonu ile gösterilir buradaπ_p (q), (pq) ̅ doğrusunun q≠p için P^(n-1)’deki kestiği noktayı ifade etmektedir. Bu makalede, W belirli homojen polinomların sıfır noktalarının kümesi olduğunda, biz I(π_p (W)) ideali için üreteç kümesi bulacağız.
References
- Cox, D., Little, J., & O'Shea, D. (1996). Ideals, Varieties and Algorithms. New-York: Springer Cham. https://doi.org/10.1007/978-3-319-16721-3
- Decker, W.; Gruel, G.; Pfister, G. (1999). Primary Decomposition: Algorithms and Comparisons. Algorithms Algebra and Number Theory, 187-220. https://doi.org/10.1007/978-3-642-59932-3_10
- Greuel, G. M., & Pfister, G. (2008). A Singular Introduction to Commutative Algebra. Springer Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73542-7
- Harris, J. (1992). Algebraic Geometry. New York: Springer New York, NY. https://doi.org/10.1007/978-1-4757-2189-8
- Kemper, G. (2002). The Calculation of Radical Ideals In Positive Characteristic. J. Symbolic Computation, 34(3), 229-238. https://doi.org/10.1006/jsco.2002.0560
Abstract
Consider a projective variety W⊆P^n and a point p∈P^n\W. The projection at point p onto P^(n-1) is represented by the mapping π_p:P^n\{p}→P^(n-1), where π_p (q) denotes the point of intersection between the line (pq) ̅ and P^(n-1), for q≠p. In this article, we derive a generator set for the ideal I(π_p (W)) when W is defined as the set of zero points of certain homogeneous polynomials.
References
- Cox, D., Little, J., & O'Shea, D. (1996). Ideals, Varieties and Algorithms. New-York: Springer Cham. https://doi.org/10.1007/978-3-319-16721-3
- Decker, W.; Gruel, G.; Pfister, G. (1999). Primary Decomposition: Algorithms and Comparisons. Algorithms Algebra and Number Theory, 187-220. https://doi.org/10.1007/978-3-642-59932-3_10
- Greuel, G. M., & Pfister, G. (2008). A Singular Introduction to Commutative Algebra. Springer Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73542-7
- Harris, J. (1992). Algebraic Geometry. New York: Springer New York, NY. https://doi.org/10.1007/978-1-4757-2189-8
- Kemper, G. (2002). The Calculation of Radical Ideals In Positive Characteristic. J. Symbolic Computation, 34(3), 229-238. https://doi.org/10.1006/jsco.2002.0560
Details
| Primary Language | English |
|---|---|
| Subjects | Algebra and Number Theory |
| Journal Section | Natural Sciences and Mathematics / Fen Bilimleri ve Matematik |
| Authors | |
| Publication Date | December 31, 2024 |
| Submission Date | March 11, 2024 |
| Acceptance Date | August 26, 2024 |
| Published in Issue | Year 2024 Volume: 29 Issue: 3 |
