Some remarks on smooth projective varieties of small degree and codimension
Abstract
Abstract The purpose of this note is twofold. First, we give a quick proof of Ballico–Chiantini’s theorem stating that a Fano or Calabi–Yau variety of dimension at least 4 in codimension 2 is a complete intersection. Second, we improve Barth–Van de Ven’s result asserting that if the degree of a smooth projective variety of dimension n is less than approximately $$0.63 \cdot n^{1/2},$$ 0.63 · n 1 / 2 , then it is a complete intersection. We show that the degree bound can be improved to approximately $$0.79 \cdot n^{2/3}.$$ 0.79 · n 2 / 3 .
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Commutative Algebra and Its Applications
Geometry and complex manifolds
Publication details
- Journal / source
- Mathematische Zeitschrift
- Volume
- 312
- Issue
- 3
- Publication date
- 12 February 2026
- Language
- EN