1992/02/12 by Walter D. Neumann, Neumann, Walter D., Lê Vǎn Thành +2
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9202008
6 pages, Plain TeX, Dec 20, 1991
arxiv created 1992/02/12 · openalex publication_date 1992/02/12 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give two proofs of a conjecture of the first author (Inv. Math. 98, 1989) that a reduced algebraic plane curve is regular at infinity if and only if its link at infinity is a regular toral link. This conjecture has also been proved by Ha H.~V. using Lojasiewicz numbers at infinity. Our first proof uses the polar invariant and the second proof uses linear systems of plane curve singularities. The second approach (based on a paper in preparation) also proves a stronger conjecture (loc. cit.) describing topologically the regular link at infinity associated with an irregular link at infinity.