Are Abelian varieties smooth?

Excuse me, could you please elaborate on the concept of Abelian varieties and whether they are indeed smooth? I'm particularly intrigued by the geometric and algebraic properties that define them, and how these factors contribute to their smoothness. Additionally, I'm curious about any mathematical proofs or theorems that support or refute this notion. I'm looking forward to a comprehensive explanation that sheds light on this fascinating aspect of algebraic geometry.