Kawaguchi-Silverman Conjecture for Projectivized Bundles over Curves

Sasha Zotine, Queen's University

The Kawaguchi-Silverman Conjecture (KSC) is a recent conjecture equating two invariants of a dominant rational map between projective varieties: the first dynamical degree and arithmetic degree. The first dynamical degree measures the topological mixing of the map, and the arithmetic degree measures how complicated rational points become after iteration. Recently, the conjecture was established for several classes of varieties, including projectivized bundles over any non-elliptic curve. We will discuss my recent work with Brett Nasserden to resolve the elliptic case, hence proving KSC for all projectivized bundles over curves. 

QNC 2501