Sharp slope bounds for sweeping families of trigonal curves

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We establish sharp bounds for the slopes of curves in Mg that sweep the locus of trigonal curves, proving Stankova-Frenkel's conjectured bound of 7+6/g for even g and obtaining the bound 7+20/(3g+1) for odd g. For even g, we find 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 effective divisor and give a similar explicit expression.