2001/04/17 by Jonathan Wahl, Wahl, Jonathan
Mathematics · #14D15 #14J32 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #math.AG #msc:14D15 #msc:14J32
paper · pdf · doi:10.48550/arxiv.math/0104172
21 pages
arxiv created 2001/04/17 · openalex publication_date 2001/04/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Theorem: If W is a smooth complex projective variety with h1 (O-scriptW) = 0, then a sufficiently ample smooth divisor X on W cannot be a hyperplane section of a Calabi-Yau variety, unless W is itself a Calabi-Yau. Corollary: A smooth hypersurface of degree d in Pn (n >= 2) is a hyperplane section of a Calabi-Yau variety iff n+2 <= d <= 2n+2. The method is to construct out of the variety W a universal family of all varieties Z for which X is a hyperplane section with normal bundle KX, and examine the "bad" singularities of such Z. A motivation is to show many curves cannot be divisors on a K-3 surface.