Vasily Rogov

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math.AG2026

Topology of higher Albanese maps and aspherical varieties with nilpotent fundamental group

Vasily Rogov

Let $X$ be a normal complex algebraic variety. Let $G_{Z}^{s} (X)$ be the maximal torsion free nilpotent quotient of $I ¨ _{1} (X)$ of nilpotency class at most $s$ . Let…

math.AG2025

O-minimal geometry of higher Albanese manifolds

Vasily Rogov

Let X be a normal quasi-projective variety over $C$ . We study its higher Albanese manifolds, introduced by Hain and Zucker, from the point of view of o-minimal geometry. W…

math.AG2025

The Bieri-Neumann-Strebel sets of quasi-projective groups

Vasily Rogov

Let $X$ be a smooth complex quasi-projective variety and $I^ = I ¨ _{1} (X)$ . Let $I ¨ : I^ \to R$ be an additive character. We prove that the ray $[I ¨ ]$ does not belong to the…