Height zeta functions of toric bundles over flag varieties

Height Zeta Functions of Toric Bundles over Flag Varieties

Lectures on Height Zeta Functions of Toric Varieties

— We explain the main ideas and techniques involved in recent proofs of asymptotics of rational points of bounded height on toric varieties.

Automorphisms of Certain Projective Bundles over Toric Varieties

The purpose of this note is to exhibit the automorphism group of a projective bundle P(E) over a simplicial toric variety X when the bundle E is a direct sum of equvariant line bundles. This case is important in the study of moduli of complete intersections on toric varieties including projective spaces. The main result is that the automorphism group of P (E) is, up to a finite group, the semi-...

Height Zeta Functions of Twisted Products

We investigate analytic properties of height zeta functions of toric bundles over flag varieties.

Partial Zeta Functions of Algebraic Varieties over Finite Fields

Motivated by arithmetic applications, we introduce the notion of a partial zeta function which generalizes the classical zeta function of an algebraic variety defined over a finite field. We then explain two approaches to the general structural properties of the partial zeta function in the direction of the Weil type conjectures. The first approach, using an inductive fibred variety point of vi...