The final log canonical model of the moduli space of stable curves of\n genus four

2011/06/24 by Maksym Fedorchuk, Fedorchuk, Maksym · 2 citations
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Mathematical Dynamics and Fractals

paper · pdf · doi:10.48550/arxiv.1106.5012

openalex publication_date 2011/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the final log canonical model of the moduli space of stable\ncurves of genus four. We prove that the rational map from \M₄ to this\nmodel contracts the Petri and the boundary divisors and flips the hyperelliptic\nlocus. As an application, we find an exact bound on slopes of moving divisors\non \M₄.\n

Citations

• Log minimal model program for the moduli space of stable curves: The first flip

Cited by

• Effective divisors on moduli spaces of curves and abelian varieties
• Remarks on two problems by Hassett

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