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David A. Cox coauthored a systematic text on toric varieties with John B. Little and Hal Schenck. The subject connects algebraic geometry with the geometry of polyhedra: convex cones and a fan in toric geometry encode affine pieces and their gluings. The book develops this combinatorial description alongside divisors, homogeneous coordinates and line bundles.^[ref]

Hal Schenck coauthored a text on toric varieties with David A. Cox and John B. Little. It develops the bridge between the geometry of polyhedra and algebraic geometry, including the construction of varieties from a fan in toric geometry and the study of their divisors and line bundles. Combinatorial data thereby become tools for geometric calculations.^[ref]

By David A. Cox, John B. Little and Hal Schenck. American Mathematical Society, 2011. Author book page: dacox.people.amherst.edu/toric.html . Consulted draft: web.ma.utexas.edu/users/ikmartin/pages/additional-pages/toric-page/documents/Toric-Varieties_Cox-Little-Schenck.pdf . Chapters 1–3 give cones, normal toric varieties and orbits; chapters 4–6 treat divisors, homogeneous coordinates and line bundles.