For several graph families of stable curves built from rational components, the associated conic is non-split, which implies the universal genus g curve has period and index 2g-2.
Principal homogeneous spaces over abelian varieties
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Conics associated with totally degenerate curves
For several graph families of stable curves built from rational components, the associated conic is non-split, which implies the universal genus g curve has period and index 2g-2.