Cartwright–Sturmfels Hilbert schemes
Abstract
Abstract Let be the Cox ring of a product of projective spaces. In this paper, we study the Cartwright–Sturmfels Hilbert schemes of , which are multigraded Hilbert schemes that parameterize only radical ideals. Our main result shows that these Hilbert schemes are always smooth and irreducible if the Picard rank is at most 2. This result can be seen as a multigraded analogue of the famous theorems of Fogarty and Maclagan–Smith, where the Picard rank replaces the dimension of the ambient space.
Fields of Study & Subjects
Matrix Theory and Algorithms
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- Journal of the London Mathematical Society
- Volume
- 114
- Issue
- 3
- Publication date
- 1 September 2026
- Language
- EN