Birational geometry of moduli spaces of stable objects on Enriques\n surfaces

2018/10/04 by Thorsten Beckmann, Beckmann, Thorsten
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1810.02165

openalex publication_date 2018/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using wall-crossing for K3 surfaces, we establish birational equivalence of\nmoduli spaces of stable objects on generic Enriques surfaces for different\nstability conditions. As an application, we prove in the case of a Mukai vector\nof odd rank that they are birational to Hilbert schemes. The argument makes use\nof a new Chow-theoretic result, showing that moduli spaces on an Enriques\nsurface give rise to constant cycle subvarieties of the moduli spaces of the\ncovering K3.\n

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