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We establish sharp bounds for the slopes of curves in Mg that sweep out the locus of trigonal curves, reproving Stankova-Frenkel's bound of 7+6=g for even g and obtaining the bound 7+20=(3g +1) for odd g. For even g, we nd an explicit expression of the so-called Maroni divisor in the Picard group of the space of admissible triple covers. For odd g, we describe the analogous extremal eective divisor and give a similar explicit expression.

Sharp slope bounds for sweeping families of trigonal curves