Semi-continuity of Complex Singularity Exponents in Singular Central Fiber Cases

TL;DR

This paper extends the understanding of complex singularity exponents by proving semi-continuity in cases where the central fiber has more complex singularities, broadening previous results.

Contribution

It provides a proof of semi-continuity of complex singularity exponents for singular central fibers, including non-normal crossing cases, which was not previously established.

Findings

Proved semi-continuity for complex singularity exponents with singular central fibers.

Extended previous results to more general singular fiber cases.

Corrected earlier typos in the proof.

Abstract

In this new version, we add the proof of the main theorem when the central fiber is not necessarily simple normal crossing. We also correct some typos.