Polynomials with integral coefficients, equivalent to a given polynomial
Author:
János Kollár
Journal:
Electron. Res. Announc. Amer. Math. Soc. 3 (1997), 17-27
MSC (1991):
Primary 11G35, 14G25, 14D10; Secondary 11C08, 11E12, 11E76, 11R29, 14D25, 14J70
DOI:
https://doi.org/10.1090/S1079-6762-97-00019-X
Published electronically:
April 8, 1997
MathSciNet review:
1445631
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Abstract: Let $f(x_{0},\dots ,x_{n})$ be a homogeneous polynomial with rational coefficients. The aim of this paper is to find a polynomial with integral coefficients $F(x_{0},\dots ,x_{n})$ 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.
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Additional Information
János Kollár
Affiliation:
University of Utah, Salt Lake City, UT 84112
MR Author ID:
104280
Email:
kollar@math.utah.edu
Keywords:
Polynomials,
hypersurfaces,
geometric invariant theory,
class numbers,
quadratic forms
Received by editor(s):
January 30, 1997
Published electronically:
April 8, 1997
Communicated by:
Robert Lazarsfeld
Article copyright:
© Copyright 1997
American Mathematical Society