Hyperplane sections of linearly normal curves

Reducible Hyperplane Sections I

Hyperplane Sections of Abelian Surfaces

By a theorem of Wahl, the canonically embedded curves which are hyperplane section of K3 surfaces are distinguished by the non-surjectivity of their Wahl map. In this paper we address the problem of distinguishing hyperplane sections of abelian surfaces. The somewhat surprising result is that the Wahl map of such curves is (tendentially) surjective, but their second Wahl map has corank at least...

Hyperplane Sections and Derived Categories

We give a generalization of the theorem of Bondal and Orlov about the derived categories of coherent sheaves on intersections of quadrics revealing its relation to projective duality. As an application we describe the derived categories of coherent sheaves on Fano 3-folds of index 1 and degrees 12, 16 and 18.

Hyperplane Sections of Calabi-yau Varieties

Theorem. If W is a smooth complex projective variety with h(OW ) = 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 ≥ 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 ...

Hyperplane sections in arithmetic hyperbolic manifolds

In this paper, we prove that the homology groups of immersed totally geodesic hypersurfaces of compact arithmetic hyperbolic manifolds virtually inject in the homology group of the