Toric degenerations and Calabi-Yau orbifolds

自从Gross和Siebert在2007年发现了退化的Calabi-Yau流形的正则光滑以来，环向退化和仿射流形的科学规划已经被认为是理解Calabi-Yau流形镜像对称的复杂参数侧的正确框架。该提案涉及该程序的重要应用，以回答上同调和枚举问题。我打算了解Kahler参数在弦上同调的推测定义中的作用，并构建一个关于confold转换的热带观点。在这两种情况下，轨道型卡拉比-丘的退化都起着重要作用。

Since the discovery of canonical smoothing for a degenerate Calabi-Yau manifold by Gross and Siebert in 2007, the scientific program of toric degenerations and affine manifolds has become recognized as the right framework to understand the complex parameter side of the mirror Symmetry of Calabi-Yau manifolds. The proposal concerns important applications of the program to answer cohomological and enumerative questions. I intend to gain an understanding of the role of the Kahler parameters in the conjectural definition of string cohomology and to construct a tropical point of view on conifold transitions. Degenerations of orbifold Calabi-Yau s play an essential role in both of these.