2024/11/21 by Anand Deopurkar, Deopurkar, Anand, Anand Patel +1 · 1 citation
Computer Science · Mathematics · #14N10 #14N15 #14N25 #51N35 #Algebraic Geometry (math.AG) #Commutative Algebra and Its Applications #Computational Geometry and Mesh Generation #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.2411.14232
openalex publication_date 2024/11/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper culminates in the count of the number of 3-Veronese surfaces passing through 13 general points. This follows the case of 2-Veronese surfaces discovered by Coble in the 1920's. One important element of the calculation is a direct construction of a space of "complete triangles." Our construction is different from the classical ordered constructions of Schubert, Collino and Fulton, as it occurs directly on the Hilbert scheme of length 3 subschemes of the plane. We transport the enumerative problem into a 26-dimensional Grassmannian bundle over our space of complete triangles, where we perform Atiyah-Bott localization. Several important questions arise, which we collect at the end of the paper.