Reflective hyperbolic 2-elementary lattices, K3 surfaces and hyperkahler varieties

2022/09/19 by Alexeev, Valery
#14J28 #20F55 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2209.09110

Abstract

We compute Coxeter diagrams of several ``large'' reflective even 2-elementary hyperbolic lattices and their maximal parabolic subdiagrams, and give some applications of these results to the theory of K3 surfaces and hyperkahler varieties.

Related

• On the classification of hyperbolic root systems of the rank three. Part II
• Hyperbolic reflection groups associated to the quadratic forms -3x₀² + x₁² + ... + x_n²
• From geometry to arithmetic of compact hyperbolic Coxeter polytopes
• On the classification of hyperbolic root systems of the rank three. Part III
• Effective bounds for Vinberg's algorithm for arithmetic hyperbolic lattices