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- Schubert_calculus abstract "In mathematics, Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert, in order to solve various counting problems of projective geometry (part of enumerative geometry). It was a precursor of several more modern theories, for example characteristic classes, and in particular its algorithmic aspects are still of current interest. The objects introduced by Schubert are the Schubert cells, which are locally closed sets in a Grassmannian defined by conditions of incidence of a linear subspace in projective space with a given flag. For details see Schubert variety.The intersection theory of these cells, which can be seen as the product structure in the cohomology ring of the Grassmannian of associated cohomology classes, in principle allows the prediction of the cases where intersections of cells results in a finite set of points; which are potentially concrete answers to enumerative questions. A supporting theoretical result is that the Schubert cells (or rather, their classes) span the whole cohomology ring.In detailed calculations the combinatorial aspects enter as soon as the cells have to be indexed. Lifted from the Grassmannian, which is a homogeneous space, to the general linear group that acts on it, similar questions are involved in the Bruhat decomposition and classification of parabolic subgroups (by block matrix).Putting Schubert's system on a rigorous footing is Hilbert's fifteenth problem.".
- Schubert_calculus wikiPageExternalLink Kleiman-Laksov.pdf.
- Schubert_calculus wikiPageID "3061740".
- Schubert_calculus wikiPageRevisionID "599720330".
- Schubert_calculus first "Frank".
- Schubert_calculus hasPhotoCollection Schubert_calculus.
- Schubert_calculus id "S/s130080".
- Schubert_calculus last "Sottile".
- Schubert_calculus subject Category:Algebraic_geometry.
- Schubert_calculus subject Category:Topology_of_homogeneous_spaces.
- Schubert_calculus comment "In mathematics, Schubert calculus is a branch of algebraic geometry introduced in the nineteenth century by Hermann Schubert, in order to solve various counting problems of projective geometry (part of enumerative geometry). It was a precursor of several more modern theories, for example characteristic classes, and in particular its algorithmic aspects are still of current interest.".
- Schubert_calculus label "Schubert calculus".
- Schubert_calculus sameAs m.08ny8m.
- Schubert_calculus sameAs Q7432936.
- Schubert_calculus sameAs Q7432936.
- Schubert_calculus wasDerivedFrom Schubert_calculus?oldid=599720330.
- Schubert_calculus isPrimaryTopicOf Schubert_calculus.