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Stability of pencils of plane quartic curves

Edoardo Ballico, Paolo Oliverio (1983)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

In questa nota si danno dei criteri per la stabilità di fasci di quartiche piane.

Stable reduction of three point covers

Stefan Wewers (2005)

Journal de Théorie des Nombres de Bordeaux

This note gives a survey of some recent results on the stable reduction of covers of the projective line branched at three points.

Stable twisted curves and their r -spin structures

Alessandro Chiodo (2008)

Annales de l’institut Fourier

The subject of this article is the notion of r -spin structure: a line bundle whose r th power is isomorphic to the canonical bundle. Over the moduli functor M g of smooth genus- g curves, r -spin structures form a finite torsor under the group of r -torsion line bundles. Over the moduli functor M ¯ g of stable curves, r -spin structures form an étale stack, but both the finiteness and the torsor structure are lost.In the present work, we show how this bad picture can be definitely improved just by placing...

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