PreprintCC0arXiv
Xiao's Genus-Two Fibration: Branched Covers and Braid Monodromy
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.
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BibTeX
@misc{akhmedov2026xiaos,
title = {{Xiao's Genus-Two Fibration: Branched Covers and Braid Monodromy}},
author = {Anar Akhmedov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.17634},
eprint = {2609.17634},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.17634},
note = {CC0},
}
RIS
TY - UNPB
TI - Xiao's Genus-Two Fibration: Branched Covers and Braid Monodromy
AU - Anar Akhmedov
PY - 2026
DA - 2026/09/15
PB - arXiv
DO - 10.48550/arxiv.2609.17634
UR - https://arxiv.org/abs/2609.17634
AB - 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.
ER -