Theorem of the cube Theorem of the cube In mathematics, the theorem of the cube is a condition for a line bundle over a product of three complete varieties to be trivial. It was a principle discovered, in the context of linear equivalence, by the Italian school of algebraic geometry. The final version of the theorem of the cube was first published by , who credited it to André Weil. A discussion of the history has been given by . A treatment by means of sheaf cohomology, and description in terms of the Picard functor, was given by . The theorem states that for
Cube 2: Sauerbraten episodic gameplay and deathmatches on multiplayer maps with AI bots instead of human opponents. Cube 2: Sauerbraten started as a redesign of the original "Cube" game engine. The "Cube 2: Sauerbraten" engine is written in C++ and OpenGL. "Cube 2: Sauerbraten" shares most of its design goals and philosophy with its predecessor, but using a new 6-directional heightfield (or octree) world model. Its first, developer-only, release was made on February 27, 2004. One of the latest releases, dubbed the "Justice Edition", debuted on July 19, 2010, adding two new player models, thirty new user-created maps, several new game modes, including