2017/11/28 by Muhammad Imran Qureshi, Qureshi, Muhammad Imran · 2 citations
Mathematics · #14J10 #14J45 #14M07 #14Q10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.1711.10222
openalex publication_date 2017/11/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct biregular models of families of log Del Pezzo surfaces with rigid cyclic quotient singularities such that a general member in each family is wellformed and quasismooth. Each biregular model consists of infinite series of such families of surfaces; parameterized by the natural numbers ℕ. Each family in these models is represented by either a codimension 3 Pfaffian format modelled on the Plücker embedding of Gr(2,5) or a codimension 4 format modelled on the Segre embedding of \(ℙ2 × ℙ2 \). In particular, we show the existence of two biregular models in codimension 4 which are bi parameterized, giving rise to an infinite series of models of families of log Del Pezzo surfaces. We identify those models of surfaces which do not admit a \(\mathbb Q\)-Gorenstein deformation to a toric variety.