Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8896515 | Journal of Algebra | 2018 | 12 Pages |
Abstract
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,â¯,dk) containing a rational curve has codimension at least âi=1kdiâ2n+2 and give similar results for hypersurfaces containing higher genus curves.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Eric Riedl, Matthew Woolf,