2022 ON THE STABILITY OF BINARY FORMS AND THEIR WEIGHTED HEIGHTS
Elira Curri
Author Affiliations +
Albanian J. Math. 16(1): 3-23 (2022). DOI: 10.51286/albjm/1656410487

Abstract

Let k be a number field, Ok its ring of integers, and f(x,y)Ok[x,y] an integral binary form of degree d3. Minimality of f(x,y) is equivalent to residual semistability. In this paper, we give a method to explicitly determine a binary form, k-equivalent to f, which is residually semistable. for any prime pOk.

In the last part of the paper we compare the GIT height from [Zha96] with weighted height in [BGS20] and show that for strictly semistable forms their logarithmic weighted height 𝔰k>0, for d0. Moreover, we show that binary forms with logarithmic weighted height 𝔰k(ξ(f))=0 exist for any degree d3.

Citation

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Elira Curri. "ON THE STABILITY OF BINARY FORMS AND THEIR WEIGHTED HEIGHTS." Albanian J. Math. 16 (1) 3 - 23, 2022. https://doi.org/10.51286/albjm/1656410487

Information

Published: 2022
First available in Project Euclid: 11 July 2023

MathSciNet: MR4448533
zbMATH: 07551377
Digital Object Identifier: 10.51286/albjm/1656410487

Subjects:
Primary: 14H10 , 20F70
Secondary: 14H37 , 14Q05

Keywords: binary forms , stability , weighted heights

Rights: Copyright © 2022 Research Institute of Science and Technology (RISAT)

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Vol.16 • No. 1 • 2022
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