Orbifold Fundamental Groups of Log Calabi-Yau Surface Pairs, and the Jordan Constant

Explore the intricacies of orbifold fundamental groups in log Calabi-Yau surface pairs through this comprehensive lecture by Cécile Gachet. Delve into joint research with J. Moraga and Z. Liu, examining the concept of orbifold fundamental group π1(X, D) for pairs (X,D), where X is a complex projective normal variety and D an effective Q-Weil divisor with coefficients in [0, 1]. Discover how normal subgroups of finite index in this group parametrize finite Galois covers of X, with branching controlled by D's coefficients. Investigate the properties of orbifold fundamental groups for Calabi-Yau surface pairs with log canonical singularities, including the existence of a normal subgroup with specific index, nilpotency length, and total rank constraints. Explore the proof methodology, which incorporates results on fundamental group finiteness, Minimal Model Program in dimension 2, and analysis of various surface types. Gain insights into pairs with virtually nilpotent but not virtually abelian fundamental groups, and understand the significance of the Jordan constant of 3Bir(P2) in this context.