Isoresidual fibration and resonance arrangements
组织者
演讲者
时间
2024年03月13日 13:30 至 15:30
地点
A3-1-101
线上
Zoom 928 682 9093
(BIMSA)
摘要
Meromorphic 1-forms on the Riemann sphere with prescribed orders of singularities form strata endowed with period coordinates. Fixing residues at the poles defines a fibration of any stratum to the vector space of configurations of residues. In a joint work with Quentin Gendron, it has been proved that for strata of 1-forms with only one zero, the isoresidual fibration is a cover of the space of configurations of residues ramified over an arrangement of complex hyperplanes called the resonance arrangement. Using combinatorics of decorated tree and the dictionary between complex analysis and flat geometry, we give a formula to compute the degree of this cover and investigate its monodromy. In a more recent work with Dawei Chen, Quentin Gendron and Miguel Prado, we investigate the case of strata with two zeroes where isoresidual fibers are complex curves endowed with a canonical translation structure. Singularities of this structure provide topological invariants of the fibers that refine the Euler characteristic and still lack an interpretation in terms of enumerative geometry.
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.