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arXiv · 1912.08252

Varieties in $(\mathbf{P}^1(\bar{\mathbf{F}}))^n$ by Elimination and Extension

Douglas A. Leonard
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Abstract

This paper contains a theory of elimination and extension to compute varieties symbolically, based on using {\em coordinates} from $(\mathbf{P}^1(\bar{\mathbf{F}}))^n$ and disjoint {\em parts} of varieties (defined by both equality and inequality constraints), leading to a recursive algorithm to compute said varieties by extension at the level of {\em parts} of a variety. {\sc Macaulay2} code for this is included along with an example. This is a first step in the author's project of giving a purely algebraic theory of desingularization of function fields, in that that project relies heavily on using this type of coordinates for function field elements and on partitioning a set of valuations into disjoint sets similarly.

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Douglas A. Leonard. 2019-12-17. Varieties in $(\mathbf{P}^1(\bar{\mathbf{F}}))^n$ by Elimination and Extension. https://arxiv.org/abs/1912.08252

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