Deforming Geometric Transitions

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.