Bilinear secants and birational geometry of blowups of P n × P n + 1
Abstract
We introduce bilinear secant varieties and joins of subvarieties of products of projective spaces, as a generalisation of the classical secant varieties and joins of projective varieties. We show that the bilinear secant varieties of certain rational normal curves of P n × P n + 1 play a central role in the study of the birational geometry of X s n , n + 1 , its blow-up in s points in general position. We show that X s n , n + 1 is log Fano, and we compute its effective and movable cones, for s ≤ n + 2 and n ≥ 1 and for s ≤ n + 3 and n ≤ 2 , and we compute the effective and movable cones of X 6 3 , 4 .
Fields of Study & Subjects
Advanced Banach Space Theory
Mathematical Inequalities and Applications
Mathematical Approximation and Integration
Publication details
- Journal / source
- Journal of Pure and Applied Algebra
- Publisher
- Elsevier BV
- Volume
- 230
- Issue
- 3
- Pages
- 108194–108194
- Publication date
- 6 February 2026
- Language
- EN