Andreotti-Frankel-Hamm theorem for morphisms of algebraic varieties

TL;DR

This paper extends the classical Andreotti-Frankel-Hamm theorem to the setting of morphisms between algebraic varieties, providing a relative version that describes their homotopy types.

Contribution

The paper introduces a relative version of the Andreotti-Frankel-Hamm theorem for morphisms of algebraic varieties, broadening its applicability.

Findings

Established a relative homotopy type result for morphisms of algebraic varieties.

Generalized the classical theorem to a broader algebraic geometric context.

Abstract

The classical Andreotti-Frankel-Hamm theorem reads: a complex affine algebraic variety B, of dim_\C B=n, has homotopy type of dim_\R\le n. We prove the relative version for morphisms X\to B.