An exceptional divisor is a specific type of divisor that appears in the context of a blow-up, typically representing the preimage of a point in a projective variety when singularities are resolved. This concept is crucial in understanding how we can modify a variety to eliminate singular points and obtain a smoother structure. Exceptional divisors play a significant role in algebraic geometry, especially in the resolution of singularities where they help track the changes in the space during this modification process.
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