A lifted square formulation for certifiable Schubert calculus
For researchers in numerical algebraic geometry, this provides a more efficient formulation for certifying solutions to Schubert problems, though it is an incremental improvement over existing square formulations.
The authors propose a lifted square formulation for Schubert calculus problems that reduces the number of equations and variables compared to prior formulations, enabling more efficient certification of numerical computations via Smale's α-theory.
Formulating a Schubert problem as the solutions to a system of equations in either Plücker space or in the local coordinates of a Schubert cell usually involves more equations than variables. Using reduction to the diagonal, we previously gave a primal-dual formulation for Schubert problems that involved the same number of variables as equations (a square formulation). Here, we give a different square formulation by lifting incidence conditions which typically involves fewer equations and variables. Our motivation is certification of numerical computation using Smale's α-theory.