Sottile, Frank2024-04-262024-04-262002-01https://hdl.handle.net/20.500.14394/34272This is a pre-published version harvested from ArXiv.org. The published version can be found at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.mmj/1070919565We 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 are enumerative in all characteristics. Existing transversality results do not apply to these enumerative problems, emphasizing the need for additional theoretical work on transversality. We also strengthen some results in enumerative real algebraic geometry.Physical Sciences and Mathematicsarticle