Schubert Calculus and the Homology of the Peterson Variety
Copyright policy )Schubert Calculus and the Homology of the Peterson Variety
We use the tight correlation between the geometry of the Peterson variety and the combinatorics the symmetric group to prove that homology of the Peterson variety injects into the homology of the flag variety. Our proof counts the points of intersection between certain Schubert varieties in the full flag variety and the Peterson variety, and shows that these intersections are proper and transverse.
- Florida Gulf Coast University United States
Peterson variety, intersection theory, Schubert calculus, Classical problems, Schubert calculus, Classical real and complex (co)homology in algebraic geometry, Grassmannians, Schubert varieties, flag manifolds, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
Peterson variety, intersection theory, Schubert calculus, Classical problems, Schubert calculus, Classical real and complex (co)homology in algebraic geometry, Grassmannians, Schubert varieties, flag manifolds, Intersection theory, characteristic classes, intersection multiplicities in algebraic geometry
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