Multiple fibers of holomorphic Lagrangian fibrations

TL;DR

This paper classifies the possible multiplicities of singular fibers in holomorphic Lagrangian fibrations with components of Fujiki class, revealing they are at most 6 and linked to Kodaira types.

Contribution

It provides a complete classification of fiber multiplicities in such fibrations, connecting them to the characteristic cycle types.

Findings

Multiplicities are at most 6.

Possible multiplicities are related to Kodaira types.

All components are of Fujiki class.

Abstract

We determine all possible multiplicities of general singular fibers of a holomorphic Lagrangian fibration, under the assumption that all components of the fibers are of Fujiki class. The multiplicities are at most 6 and the possible values are intricately related to the Kodaira type of the characteristic cycle.