#### Vol. 8, No. 5, 2014

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The final log canonical model of $\overline{\mathcal{M}}_6$

### Fabian Müller

Vol. 8 (2014), No. 5, 1113–1126
##### Abstract

We describe the birational model of ${\overline{\mathsc{ℳ}}}_{6}$ given by quadric hyperplane sections of the degree-$5$ del Pezzo surface. In the spirit of the genus-$4$ case treated by Fedorchuk, we show that it is the last nontrivial space in the log minimal model program for ${\overline{\mathsc{ℳ}}}_{6}$. We also obtain a new upper bound for the moving slope of the moduli space.

##### Keywords
moduli space of curves, genus 6, log canonical model, moving slope
##### Mathematical Subject Classification 2010
Primary: 14H10
Secondary: 14E30, 14H45
##### Milestones
Received: 17 June 2013
Revised: 6 April 2014
Accepted: 19 May 2014
Published: 16 September 2014
##### Authors
 Fabian Müller Humboldt-Universität zu Berlin Unter den Linden 6 D-10099 Berlin Germany