Mahler’s conjecture for some hyperplane sections

Reducible Hyperplane Sections I

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.

Thomas hyperplane sections for primitive Hodge classes

R. Thomas proved that the Hodge conjecture is essentially equivalent to the existence of a Thomas hyperplane section having only ordinary double points as singularities and such that the restriction of a given primitive Hodge class to it does not vanish. We show that the relations between the vanishing cycles associated to the ordinary double points of a Thomas hyperplane section have the same ...

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...

The Monodromy Conjecture for Hyperplane Arrangements

The Monodromy Conjecture asserts that if c is a pole of the local topological zeta function of a hypersurface, then exp(2πic) is an eigenvalue of the monodromy on the cohomology of the Milnor fiber. A stronger version of the conjecture asserts that every such c is a root of the Bernstein-Sato polynomial of the hypersurface. In this note we prove the weak version of the conjecture for hyperplane...