Finiteness of lattice points on varieties F(y) = F(g(

Unipotent Flows and Counting Lattice Points on Homogeneous Varieties

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Genera of Algebraic Varieties and Counting of Lattice Points

This paper announces results on the behavior of some important algebraic and topological invariants — Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. — and their associated characteristic classes, under morphisms of projective algebraic varieties. The formulas obtained relate global invariants to singularities of general complex algebraic (...

Rational points on varieties

Finiteness Properties of Locally Finite Abelian Varieties

We show that any locally finite abelian variety is generated by a finite algebra. We solve a problem posed by D. Hobby and R. McKenzie by exhibiting a nonfinitely based finite abelian algebra.

Nearest Points on Toric Varieties

We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the A-discriminant in terms of Euler obstructions. Our primary goal is the development of reliable algorithmic tools for computing the points on a real toric variety that are closest to a given data point.