# Coxeter diagrams of 2-elementary K3 surfaces of genus 0, and beyond

@inproceedings{Alexeev2022CoxeterDO, title={Coxeter diagrams of 2-elementary K3 surfaces of genus 0, and beyond}, author={Valery Alexeev}, year={2022} }

. We compute the Coxeter diagrams of K3 surfaces with 2-elementary Picard lattices of genus 0 and apply them to describe their (inﬁnite) auto- morphism groups. We also compute several Coxeter diagrams of reﬂective 2-elementary hyperbolic lattices beyond the K3 case. The diagrams turn out to be remarkably symmetric, similar to the Coxeter diagrams for the unimodular lattices I 1 , 18 and I 1 , 19 found by Vinberg and Kaplinskaja.

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