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Reduction of quartic curves

Abstract

Let C be a smooth plane curve of degree 4 over a discrete valuation field. In this talk we will give necessary and sufficient conditions on the Dixmier--Ohno invariants for the curve to have (potentially) good reduction which will be either a smooth quartic or a hyperelliptic curve over the residue field. This is a joint work with C.Ritzenthaler, R. Lercier and E. Lorenzo Garcia.