Anticanonical divisor

An anticanonical divisor is a special kind of divisor in algebraic geometry related to the canonical divisor, which encodes information about a geometric object’s shape and how it twists or curves. Specifically, the anticanonical divisor is the negative of the canonical divisor, often representing global geometric or symmetry properties of a space, such as when a shape admits certain types of metric structures. It plays a key role in classifying and understanding complex varieties, especially in processes like the minimal model program, by revealing how the variety’s geometry behaves and interacts with line bundles and morphisms.