Theta divisors, resolutions and moduli of curves -- 
Gavril Farkas, October 10, 2003

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One of the defining problems in the theory of algebraic curves
in the last decades has been Green's Conjecture predicting that one can
read the intrinsic geometry of a curve from the equations of its canonical
embedding. I will describe how moduli spaces of pointed curves can be used
in a rather surprising way to prove two statements intimately related to
Green's Conjecture: the Minimal Resolution Conjecture linking the geometry
of a canonical curve to the resolution of general subsets of its points
and a conjecture of R. Lazarsfeld about the theta divisors of the powers
of the normal bundle of a curve in its Jacobian.