Algebraic Geometry
A canonical divisor is a divisor associated with a variety that encodes important geometric and topological information about the variety itself. It is often denoted by $K_X$ and can be viewed as a generalization of the notion of canonical forms in algebraic geometry, reflecting the duality between divisors and differentials. Understanding canonical divisors plays a crucial role in analyzing singularities, vanishing theorems, and applying the Riemann-Roch theorem to curves and surfaces.
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