Hyperplane sections of Calabi-Yau varieties

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dc.creatorWahl, Jonathan
dc.date2001-04-17
dc.date.accessioned2026-07-07T06:32:51Z
dc.date.available2026-07-07T06:32:51Z
dc.descriptionTheorem: If W is a smooth complex projective variety with h^1 (O-script_W) = 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 P^n (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 K_X, and examine the "bad" singularities of such Z. A motivation is to show many curves cannot be divisors on a K-3 surface.
dc.description21 pages
dc.identifierhttps://arxiv.org/abs/math/0104172
dc.identifierhttp://arxiv.org/abs/math/0104172
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98999
dc.subjectAlgebraic Geometry
dc.subject14J32, 14D15
dc.titleHyperplane sections of Calabi-Yau varieties
dc.typetext

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