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math.AG2022
Circles of Apollonius two ways
Stephen McKean
Because the problem of Apollonius is generally considered over the reals, it suffers from variance of number: there are at most eight circles simultaneously tangent to a given trio…
math.AG2020
An arithmetic enrichment of Bézout's Theorem
Stephen McKean
The classical version of Bézout's Theorem gives an integer-valued count of the intersection points of hypersurfaces in projective space over an algebraically closed field. Using wo…