The slope inequality for families in the trigonal locus

Let gg be even, let BB be a base curve not entirely contained in the Maroni divisor, and let XBX\to B be a family whose singular members belong only to Δ0TgΔ1,iTg\Delta_0\mathfrak{T}_g\cup\Delta_{1,i}\mathfrak{T}_g. The slope inequality. The slope satisfies

δλ7+6g.\frac{\delta}{\lambda}\leq 7+\frac{6}{g}.

This gives a bound for the slope of such families in the trigonal locus, under the stated restriction on the singular members and the Maroni divisor. The source supplies no resolution status beyond its presentation as a proposition.

Sources & referencesView supporting material

Primary source

Zvezdelina E. Stankova-Frenkel, “Moduli of Trigonal Curves”, arXiv:alg-geom/9710015 (1997).

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