Rational curves on complete intersections in positive characteristic

2016/09/19 by Eric Riedl, Riedl, Eric, Matthew Woolf +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1609.05958

openalex publication_date 2016/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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, ⋯, d_k) containing a rational curve has codimension at least ∑_i=1^k d_i - 2n + 2 in the moduli space of all complete intersections of given multidegree and dimension.

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