The Classification of the Stable Marked Reduction of Genus 2 Curves in Residue Characteristic 2

Consider a hyperelliptic curve of genus $2$ over a field $K$ of characteristic zero. After extending $K$ we can view it as a marked curve with its $6$ Weierstrass points. We classify the structure of the stable reduction of such curves for a valuation of residue characteristic~$2$ over a finite extension of~$K$. We implement this classification into a computer algebra system and compute it for all curves defined over $\BQ$ with conductor at most $2^{20}$.