Zariski introduced a fundamental tool for understanding linear series on surfaces known as the "Zariski decomposition." This decomposition (and its generalizations to divisors on higher dimension varieties) is frequently used in birational geometry. I will describe an analogous construction for all cycle classes. I will also give a number of examples and several geometric applications. This is joint work with A. M. Fulger.
Tuesday, September 3rd, at 4:00pm in HBH 227
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