The slope inequality for families in the trigonal locus

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Let gg be even, let BB be a base curve not entirely contained in the Maroni divisor, and let X→BX\to B be a family whose singular members belong only to Δ0Tg∪Δ1,iTg\Delta_0\mathfrak{T}_g\cup\Delta_{1,i}\mathfrak{T}_g. The slope inequality. The slope satisfies

δλ≤7+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.

References

Primary source

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

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