TL;DR
This paper explores the structure of the Calabi-Yau web through deformation equivalence of geometric transitions, aiming to identify conditions for simple, well-understood transitions in mathematics and physics.
Contribution
It introduces the concept of deformation equivalence for geometric transitions to better understand the Calabi-Yau web and analyzes conditions for simple geometric transitions.
Findings
Deformation equivalence classes organize geometric transitions.
Conditions for simple geometric transitions are identified.
Examples illustrate when simple transitions occur.
Abstract
After a quick review of the wild structure of the complex moduli space of Calabi-Yau threefolds and the role of geometric transitions in this context (the Calabi-Yau web) the concept of "deformation equivalence" for geometric transitions is introduced to understand the arrows of the Gross-Reid Calabi-Yau web as deformation-equivalence classes of geometric transitions. Then the focus will be on some results and suitable examples to understand under which conditions it is possible to get "simple" geometric transitions, which are almost the only well-understood geometric transitions both in mathematics and in physics.
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