Year: 2026
Type: article
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 .
Source: Mathematische Zeitschrift
Author: Jinhyung Park
Institution: Korea Advanced Institute of Science and Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,290
OpenAlex ID: W7128701243