The Relative Canonical Ideal of the Artin-Schreier-Kummer-Witt family of curves

2019/05/14 by Charalambous, Hara, Karagiannis, Kostas, Kontogeorgis, Aristides · 1 citation
#11G20 #14D15 #14F10 #14G17 #14G20 #14H10 #14H37 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1905.05545

Abstract

We study the canonical model of the Artin-Schreier-Kummer-Witt flat family of curves over a ring of mixed characteristic. We first prove the relative version of a classical theorem by Petri, then use the model proposed by Bertin-Mézard to construct an explicit generating set for the relative canonical ideal. As a byproduct, we obtain a combinatorial criterion for a set to generate the canonical ideal, applicable to any curve satisfying the assumptions of Petri's theorem.

Cited by

• On the de Rham cohomology of cyclic covers

Related

• A generating set for the canonical ideal of HKG-curves
• A minimal set of generators for the canonical ideal of a non-degenerate curve
• Relative Canonical Sheaves of a Family of Curves
• The canonical ideal and the deformation theory of curves with automorphisms
• Automorphisms and the canonical ideal