Height zeta functions of toric 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.

Height Zeta Functions of Twisted Products

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

Szasz Analytic Functions and Noncompact Toric Varieties

We relate the classical approximations SN (f)(x) of O.Szasz to the Bergman kernel of the Bargmann-Fock space H(C, e |z| 2 dm(z)). This relation is the analogue for compact toric varieties of the relation between Bernstein polynomials and Bergman kernels on compact toric Kähler varieties of S. Zelditch. The relation is then used to generalize the Szasz analytic functions to any infinite volume t...

Stringy Zeta Functions for Q–gorenstein Varieties

The stringy Euler number and stringy E–function are interesting invariants of log terminal singularities, introduced by Batyrev. He used them to formulate a topological mirror symmetry test for pairs of certain Calabi–Yau varieties, and to show a version of the McKay correspondence. It is a natural question whether one can extend these invariants beyond the log terminal case. Assuming the Minim...