The birational composition of arbitrary quadratic form with binary quadratic form

Q4 Mathematics
A. A. Bondarenko
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引用次数: 0

Abstract

Let f(X) and g(Y) be nondegenerate quadratic forms of dimensions m and n respectively over a field K, charK ≠ 2. Herein, the problem of the birational composition of f(X) and g(Y) is considered, namely, the condition is established when the product f(X)g(Y) is birationally equivalent over K to a quadratic form h(Z) over K of dimension m + n? The main result of this paper is the complete solution of the problem of the birational composition for quadratic forms f(X) and g(Y) over a field K when m = 2. The sufficient and necessary conditions for the existence of birational composition h(Z) for quadratic forms f(X) and g(Y) over a field K for m = 2 are obtained. The set of quadratic forms is described which can be considered as h(Z) in this case.
任意二次型与二元二次型的二元复合
设f(X)和g(Y)分别是域K上维数m和n的非简并二次型,K≠2。本文考虑f(X)与g(Y)的二元复合问题,即f(X)与g(Y)的乘积在K上二元等价于维数为m + n?本文的主要结果是完全解决了当m = 2时,二次型f(X)和g(Y)在域K上的二元复合问题。得到了在域K上,当m = 2时二次型f(X)和g(Y)的双组合h(Z)存在的充要条件。在这种情况下,二次型的集合可以被认为是h(Z)。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
0.50
自引率
0.00%
发文量
21
审稿时长
16 weeks
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