Polynomials with integral coefficients, equivalent to a given polynomial
Polynomials with integral coefficients, equivalent to a given polynomial
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具有积分系数的多项式，相当于给定的多项式
DOI：
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发表时间：
1997
期刊：
影响因子：
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通讯作者：
J. Kollár
中科院分区：
文献类型：
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作者：
J. Kollár
设f(X0，.。。，xn)是有理系数的齐次多项式。本文的目的是找出一个整系数多项式F(x0，.。。，xn)，它与f“等价”并且尽可能地“简单”。证明的主要内容是将这个问题与多项式的几何不变理论联系起来。最后给出了二元形式、类数、二次形式和三次曲面族的应用。
Let f(x0, . . . , xn) be a homogeneous polynomial with rational coefficients. The aim of this paper is to find a polynomial with integral coefficients F (x0, . . . , xn) which is “equivalent” to f and as “simple” as possible. The principal ingredient of the proof is to connect this question with the geometric invariant theory of polynomials. Applications to binary forms, class numbers, quadratic forms and to families of cubic surfaces are given at the end.