On threefolds with the smallest nontrivial monodromy group

TL;DR

This paper classifies smooth threefolds with the smallest nontrivial monodromy group acting on the second cohomology of their hyperplane sections, confirming a long-standing conjecture by providing a complete list.

Contribution

It provides the first complete classification of such threefolds with a specific monodromy group, using advanced algebraic geometry techniques.

Findings

Complete list of threefolds with monodromy group Z/2Z

Verification of Zak's 1991 classification conjecture

Application of adjunction theory and SGA7 results

Abstract

Using an adjunction-theoretic result due to A.J.Sommese together with a proposition from SGA7, we obtain a complete list of smooth threefolds for which the monodromy group acting on $H^2$ of its smooth hyperplane section is $\mathbb Z/2\mathbb Z$. The possibility of such a classification was announced by F.L.Zak in 1991.