2000 character limit reached
The Chow-Lam Form
Published 19 Jan 2024 in math.AG and math.CO | (2401.10795v2)
Abstract: The classical Chow form encodes any projective variety by one equation. We here introduce the Chow-Lam form for subvarieties of a Grassmannian. By evaluating the Chow-Lam form at twistor coordinates, we obtain universal projection formulas. These were pioneered by Thomas Lam for positroid varieties in the study of amplituhedra, and we develop his approach further. Universal formulas for branch loci are obtained from Hurwitz-Lam forms. Our focus is on computations and applications in geometry.
- A. Cayley: On a new analytical representation of curves in space, Quarterly J. of Pure and Appl. Math. 5 (1862) 81–86.
- W.-L. Chow and B. van der Waerden: Zur algebraischen Geometrie. IX. Über zugeordnete Formen und algebraische Systeme von algebraischen Mannigfaltigkeiten, Mathematische Annalen 113 (1937) 692–704.
- D. Eisenbud and F.-O. Schreyer: Resultants and Chow forms via exterior syzygies, Journal of the American Mathematical Society 16 (2003) 537–575.
- K. Kohn: Coisotropic hypersurfaces in Grassmannians, Journal of Symbolic Computation 103 (2021) 157–177.
- T. Lam: Amplituhedron cells and Stanley symmetric functions, Commun. Math. Phys. 343 (2016) 1025–1037.
- D. Logachev: Fano threefolds of genus 6, Asian J. Math. 16 (2012) 515–560.
- B. Sturmfels: The Hurwitz form of a projective variety, J. Symbolic Comp. 79 (2017) 186–196.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.