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

Elementary transversality in the Schubert calculus in any characteristic