Counting Multiplicities in a Hypersurface over a Number Field
Algebraic Geometry
2021-01-22 v2 Number Theory
Abstract
We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to this counting function will be given in terms of the degree of the hypersurface, the dimension of the singular locus, the upper bounds of height, and the degree of the field of definition.
Keywords
Cite
@article{arxiv.1707.07183,
title = {Counting Multiplicities in a Hypersurface over a Number Field},
author = {Hao Wen and Chunhui Liu},
journal= {arXiv preprint arXiv:1707.07183},
year = {2021}
}
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23 pages