2000/02/24 by Frank Sottile, Sottile, Frank
Computer Science · Engineering · Mathematics · #14M15 #14N10 #14P99 #65H20 #Advanced Combinatorial Mathematics #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Numerical Analysis (math.NA) #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.math/0002207
openalex publication_date 2000/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present a general method for constructing real solutions to some problems in enumerative geometry which gives lower bounds on the maximum number of real solutions. We apply this method to show that two new classes of enumerative geometric problems on flag manifolds may have all their solutions be real and modify this method to show that another class may have no real solutions, which is a new phenomenon. This method originated in a numerical homotopy continuation algorithm adapted to the special Schubert calculus on Grassmannians and in principle gives optimal numerical homotopy algorithms for finding explicit solutions to these other enumerative problems.