The classification of the stable marked reduction of genus 2 curves in residue characteristic 2

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