Rational curves on complete intersections in positive characteristic

We study properties of rational curves on complete intersections in positive characteristic. It has long been known that in characteristic 0, smooth Calabi–Yau and general type varieties are not uniruled. In positive characteristic, however, there are well-known counterexamples to this statement. We...

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Bibliographic Details
Published in:Journal of algebra 2018-01, Vol.494, p.28-39
Main Authors: Riedl, Eric, Woolf, Matthew
Format: Article
Language:English
Subjects:
Characteristic p geometry
Coniveau
Hypersurfaces
Rational curves
Rationality
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Summary:We study properties of rational curves on complete intersections in positive characteristic. It has long been known that in characteristic 0, smooth Calabi–Yau and general type varieties are not uniruled. In positive characteristic, however, there are well-known counterexamples to this statement. We will show that nevertheless, a general Calabi–Yau or general type complete intersection in projective space is not uniruled. We will also show that the space of complete intersections of degree (d1,⋯,dk) containing a rational curve has codimension at least ∑i=1kdi−2n+2 and give similar results for hypersurfaces containing higher genus curves.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2017.09.025