An overview of effective normalization of a projective algebraic variety nonsingular in codimension one

被引：0

作者：

Chistov A.L. ^{[1
]}

机构：

[1] St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg

来源：

Journal of Mathematical Sciences | 2010年 / 168卷 / 3期

关键词：

Russia; Linear Equation; General Position; Algebraic Variety; Polynomial Ring;

D O I：

10.1007/s10958-010-0001-3

中图分类号：

学科分类号：

摘要：

Let V be a projective algebraic variety of degree D and dimension n nonsingular in codimension one. Then the construction of the normalization of V can be canonically reduced, within time polynomial in the size of the input and Dn0(1), to solving a linear equation aX + bY + cZ = 0 over a polynomial ring. We describe a plan of proving this result with all lemmas. Bibliography: 4 titles. © 2010 Springer Science+Business Media, Inc.

引用

页码：478 / 490

页数：12

共 4 条

[1] Chistov A.L., Polynomial complexity of the Newton-Puiseux algorithm, Lect. Notes Comput. Sci., 233, pp. 247-255, (1986)
[2] Chistov A.L., Polynomial complexity algorithm for factoring polynomials and constructing components of a variety in subexponential time, Zap. Nauchn. Semin. LOMI, 137, pp. 124-188, (1984)
[3] Chistov A.L., Double-exponential lower bound for the degree of a system of generators of a polynomial prime ideal, Algebra Analiz, 20, 6, pp. 186-213, (2008)
[4] Chistov A.L., A deterministic polynomial-time algorithm tor the first Bertini theorem, (2004)

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