Hyperplane sections of Calabi-Yau varieties

Details Hyperplane sections of Calabi-Yau varieties Hyperplane sections of Calabi-Yau varieties

2001-04-17

arxiv.org/abs/math/0104172v1

Mathematics

Algebraic Geometry

21 pages

Scientific paper

Theorem: 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.

Affiliated with

Also associated with

No associations

Rating

Hyperplane sections of Calabi-Yau varieties does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hyperplane sections of Calabi-Yau varieties, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hyperplane sections of Calabi-Yau varieties will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-484395