2012/12/13 by Jonathan D. Hauenstein, Hauenstein, Jonathan D., Nickolas Hein +3 · 1 citation
Mathematics · #14N15 #14Q20 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14N15 #msc:14Q20
paper · pdf · doi:10.48550/arxiv.1212.3315
11 pages, extended abstract
arxiv created 2012/12/13 · arxiv updated 2012/12/14
Traditional formulations of geometric problems from the Schubert calculus, either in Plucker coordinates or in local coordinates provided by Schubert cells, yield systems of polynomials that are typically far from complete intersections and (in local coordinates) typically of degree exceeding two. We present an alternative primal-dual formulation using parametrizations of Schubert cells in the dual Grassmannians in which intersections of Schubert varieties become complete intersections of bilinear equations. This formulation enables the numerical certification of problems in the Schubert calculus.