Geometric Proofs of Horn and Saturation Conjectures

Details Geometric Proofs of Horn and Saturation Conjectures Geometric Proofs of Horn and Saturation Conjectures

2002-08-13

arxiv.org/abs/math/0208107v3

Mathematics

Algebraic Geometry

36 pages, accepted for publication in the Journal of Algebraic Geometry

Scientific paper

We provide a geometric proof of the Schubert calculus interpretation of the Horn conjecture, and show how the saturation conjecture follows from it. The geometric proof gives a strengthening of Horn and saturation conjectures. We also establish transversality theorems for Schubert calculus in non-zero characteristic. Some parts of the version posted in Nov 2002 (concerning explicit invariants constructed from Schubert calculus) have been removed from this version. They have appeared separately in IMRN 2004, no. 69, pages 3709--3721 " Invariant theory of GL(n) and Intersection theory of Grassmannians"

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