2019/05/28 by Jarosław Buczyński, Nathan Ilten, Buczyński, Jarosław +3
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.1905.11860
openalex publication_date 2019/05/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In order to study projections of smooth curves, we introduce multifiltrations\nobtained by combining flags of osculating spaces. We classify all\nconfigurations of singularities occurring for a projection of a smooth curve\nembedded by a complete linear system away from a projective linear space of\ndimension at most two. In particular, we determine all configurations of\nsingularities of non-degenerate degree d rational curves in \ℙn when\nd - n \≤ 3 and d < 2n. Along the way, we describe the Schubert cycles\ngiving rise to these projections.\n We also reprove a special case of the Castelnuovo bound using these\nmultifiltrations: under the assumption d < 2n, the arithmetic genus of any\nnondegenerate degree d curve in \ℙn is at most d - n.\n