# Continuous families of divisors on symmetric powers of curves

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John Sheridan, Stony Brook University
Fine Hall 322

For X a smooth projective variety, we consider its set of effective divisors in a fixed cohomology class. This set naturally forms a projective scheme and if X is a curve, this scheme is a smooth, irreducible variety (fibered in linear systems over the Picard variety). However, when X is of higher dimension, this scheme can be singular and reducible. We study its structure explicitly when X is a symmetric power of a curve.