On the topology of isoresidual fibers
组织者
演讲者
时间
2025年03月13日 13:30 至 14:30
地点
A3-2a-201
摘要
Meromorphic 1-forms on the Riemann sphere, with prescribed orders of singularities, form strata equipped with period coordinates. Fixing the residues at the poles defines the isoresidual fibration of any given stratum onto the vector space of residue configurations.
In a joint work with Dawei Chen, Quentin Gendron and Miguel Prado, we show that for strata with two zeroes, isoresidual fibers are complex curves endowed with a canonical translation structure. The singularities of these fibers encode, through their local invariants, the corresponding degenerations of the parametrized objects in the multi-scale boundary. In particular, computing the genus of the underlying complex curve is reduced to a purely combinatorial problem.
As an application, we provide the classification of connected components of generic isoresidual fibers for strata with an arbitrary number of zeroes.
演讲者介绍
Tahar是BIMSA助理研究员。在加入BIMSA之前，他曾在魏茨曼科学研究所担任高级博士后研究员。他致力于平面上各种几何结构的模空间研究，包括平移和扩张结构、平坦度规和锥球度规。Guillaume-Tahar最近的研究兴趣涉及线性微分算子、isoresidual fibrations和simplicial arrangements of lines.