Stability and semi-stability of (2,2)-type surfaces

2020/09/14 by A. J. Parameswaran, Parameswaran, A. J., Nabanita Ray +1 · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2009.06232

openalex publication_date 2020/09/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We describe the GIT compactification of the moduli of (2,2)-type effective divisors of ℙ¹×ℙ² (i.e., surfaces of the linear system \vert π₁^*O_ℙ¹(2)⊗ π₂^*O_ℙ²(2)\vert ) which are generically Del Pezzo surfaces of degree two. In order to get the compactification, we characterize stable and semi-stable (2,2)-type surfaces, and also determine the equivalence classes of strictly semi-stable (2,2)-type surfaces. Moreover, we describe the boundary of the moduli of (2,2)-type surfaces.

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