Elementary Algebraic Geometry
Resolution of singularities is a process in algebraic geometry that aims to replace a singular algebraic variety with a non-singular one, allowing for the study of its geometric properties in a more manageable way. This process often involves techniques such as blowing up, which helps to resolve points where the variety fails to be well-defined or smooth. By resolving these singularities, mathematicians can better understand the behavior of curves and surfaces, and their intersections, in higher-dimensional spaces.
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