Stable pair compactifications of the moduli space of degree one del pezzo surfaces via elliptic fibrations

2018/02/02 by Kenneth Ascher, Ascher, Kenneth, Dori Bejleri +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1802.00805

openalex publication_date 2018/02/02 · openalex created_date 2018/02/23 · openalex updated_date 2026/07/28

Abstract

A degree one del Pezzo surface is the blowup of P² at 8 general points. By the classical Cayley-Bacharach Theorem, there is a unique 9th point whose blowup produces a rational elliptic surface with a section. Via this relationship, we construct a stable pair compactification of the moduli space of anti-canonically polarized degree one del Pezzo surfaces.

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