### University of Arkansas Topology Seminar: 5/4/2023

### Speaker: Sümeyra Sakalli

### Title: Singular Fibers in algebraic fibrations of genus two and their monodromy factorizations

Kodaira classified all singular fibers that can arise in algebraic elliptic fibrations. Later, Ogg, Iitaka and then Namikawa and Ueno gave a classification for genus two fibrations. In this work, we split these algebraic genus two fibrations into Lefschetz fibrations and determine the monodromies. More specifically, we look at four families of hypersurface singularities in ℂ^{3}. Each hypersurface comes equipped with a fibration by genus 2 algebraic curves which degenerate into a single singular fiber. We determine the resolution of each of the singularities in the family and find a flat deformation of the resolution into simpler pieces, resulting in a fibration of Lefschetz type. We then record the description of the Lefschetz fibration as a positive factorization in Dehn twists. This gives us a dictionary between configurations of curves and monodromy factorizations for some singularities of genus two fibrations. This is joint work with J. Van Horn-Morris.

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