Year: 2026
Type: preprint
Abstract: We compute the geometric monodromy factorization of Xiao's genus-two Lefschetz fibration directly from its branched-cover construction, following Moishezon's braid-monodromy method. The complete quadrangle determines the motion of the six branch points and gives four nonseparating and three separating vanishing cycles. At each of the three $3+3$ degenerations, the branch motion determines the spherical mapping class, and Xiao's local holomorphic model determines its genus-two lift. After fixing a distinguished system of paths, we obtain an ordered positive factorization of type $(4,3)$ and give Artin coordinates for the seven factors.
Source: arXiv (Cornell University)
Author: Akhmedov, Anar
Institutions: University of Minnesota, Harvard University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7213504995