Rational curves on complete intersections in positive characteristic

Eric Riedl; Matthew Woolf

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arXiv · 1609.05958

Rational curves on complete intersections in positive characteristic

Eric Riedl·Matthew Woolf

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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 \emph{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 $(d_1, \cdots, d_k)$ containing a rational curve has codimension at least $\sum_{i=1}^k d_i - 2n + 2$ in the moduli space of all complete intersections of given multidegree and dimension.

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BibTeX RIS

Eric Riedl, Matthew Woolf. 2016-09-19. Rational curves on complete intersections in positive characteristic. https://arxiv.org/abs/1609.05958

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