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Polynomials with integral coefficients, equivalent to a given polynomial

Author(s): 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
Posted: April 8, 1997
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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
Email: kollar@math.utah.edu

DOI: 10.1090/S1079-6762-97-00019-X
PII: S 1079-6762(97)00019-X
Keywords: Polynomials, hypersurfaces, geometric invariant theory, class numbers, quadratic forms
Received by editor(s): January 30, 1997
Posted: April 8, 1997
Communicated by: Robert Lazarsfeld
Copyright of article: Copyright 1997, American Mathematical Society

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