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We construct Eagon--Northcott cycles on Hurwitz space and compare theirclasses to Kleiman's multiple point loci. Applying this construction towardsthe classification of Betti tables of canonical curves, we find that the valueof the extremal Betti number records the number of minimal pencils. The resultholds under transversality hypotheses equivalent to the virtual cycles having ageometric interpretation. We analyse the case of two minimal pencils, showingthat the transversality hypotheses hold generically.

Betti Numbers of Curves and Multiple-Point Loci