Projective varieties of low codimension in characteristic 𝑝>0

Speiser, Robert

doi:10.1090/S0002-9947-1978-0491703-4

Projective varieties of low codimension in characteristic $p>0$
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by Robert Speiser

Trans. Amer. Math. Soc. 240 (1978), 329-343

DOI: https://doi.org/10.1090/S0002-9947-1978-0491703-4

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Abstract:

Let X be an s-dimensional closed Cohen-Macaulay subvariety of projective n-space, over an algebraically closed field of characteristic $p > 0$. Assume $s \geqslant \tfrac {1}{2}(n + 1)$. Then (1) every stratified vector bundle on X is trivial; (2) X is simply connected. Assertion (1) generalizes Gieseker’s result for projective space, while (2) is a strengthened analogue of results of Barth and Ogus in characteristic zero.

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