Asymptotic behavior of the dimension of the Chow variety

TL;DR

This paper investigates how the dimension of the Chow variety components grows with degree, linking asymptotic behavior to cycle class positivity and providing explicit dimension calculations for projective space.

Contribution

It offers new insights into the asymptotic growth of Chow variety dimensions and computes explicit dimensions for projective space, enhancing understanding of algebraic cycle spaces.

Findings

Dimension growth rate of Chow variety components analyzed

Explicit dimension formulas for Chow variety of projective space derived

Asymptotic behavior connected to positivity of cycle classes

Abstract

We analyze the asymptotics of the dimension of components of the Chow variety as degree increases. By analogy with the divisor case, the main goal is to relate the asymptotic behavior with the positivity of the corresponding cycle classes. We also compute the dimension of the Chow variety of projective space.