2013/09/16 by Zhaorong Jin, Matilde Marcolli
Mathematics · Physics and Astronomy · #Action (physics) #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic Geometry and Number Theory #Computer science #Construct (python library) #Geometry #Geometry and complex manifolds #Logarithm #Mathematical analysis #Mathematics #Morphism #Pure mathematics #Quantum #Semigroup #Toric variety #Torus #Variety (cybernetics) #math-ph #math.AG #math.MP
paper · pdf · doi:10.1016/j.geomphys.2013.12.006
29 pages, LaTeX
arxiv created 2013/09/16 · openalex publication_date 2013/12/21 · arxiv updated 2015/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We construct endomotives associated to toric varieties, in terms of the decomposition of a toric variety into torus orbits and the action of a semigroup of toric morphisms. We show that the endomotives can be endowed with time evolutions and we discuss the resulting quantum statistical mechanical systems. We show that, in particular, one can construct a time evolution related to the logarithmic height function. We discuss relations to F1-geometry.