A small and non-simple geometric transition

TL;DR

This paper provides a detailed example of a small geometric transition that is not simple, analyzing the Kuranishi space of a Namikawa cuspidal fiber product, with implications for string theory and black hole physics.

Contribution

It presents a detailed analysis of a non-simple small geometric transition, extending previous work and clarifying its physical implications.

Findings

Improved understanding of the Kuranishi space of Namikawa cuspidal fiber products.

Identification of a geometric transition not explained by black hole condensation.

Clarification of the distinction between simple and non-simple geometric transitions.

Abstract

Following notation introduced in the recent paper \cite{Rdef}, this paper is aimed to present in detail an example of a "small" geometric transition which is not a "simple" one i.e. a deformation of a conifold transition. This is realized by means of a detailed analysis of the Kuranishi space of a Namikawa cuspidal fiber product, which in particular improves the conclusion of Y.~Namikawa in Remark 2.8 and Example 1.11 of \cite{N}. The physical interest of this example is presenting a geometric transition which can't be immediately explained as a massive black hole condensation to a massless one, as described by A.~Strominger \cite{Strominger95}.