Elementary Transversality in the Schubert calculus in any Characteristic

Details Elementary Transversality in the Schubert calculus in any Characteristic Elementary Transversality in the Schubert calculus in any Characteristic

2000-10-31

arxiv.org/abs/math/0010319v2

Michigan Math. J. 51 (2003), no. 3, 651-666

Mathematics

Algebraic Geometry

14 pages, many revisions to improve clarity

Scientific paper

We give a characteristic-free proof that general codimension-1 Schubert varieties meet transversally in a Grassmannian and in some related varieties. Thus the corresponding intersection numbers computed in the Chow (and quantum Chow) rings of these varieties are enumerative in all characteristics. We show that known transversality results do not apply to these enumerative problems, emphasizing the need for additional theoretical work on transversality. The method of proof also strengthens some results in real enumerative geometry.

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