Polarized Rigid Del Pezzo Surfaces in Low Codimension - Muhammad Imran Qureshi (Mathematics, 2020)
We provide explicit graded constructions of orbifold del Pezzo surfaces with rigid orbifold points of type <semantics><mfenced separators="" open="{" close="}">ki×1ri(1,ai):3≤ri≤10,ki∈Z≥0</mfenced></semantics> as well-formed and quasismooth varieties embedded in some weighted projective space. In particular, we present a collection of 147 such surfaces such that their image under their anti-canonical embeddings can be described by using one of the following sets of equations: a single equation, two linearly independent equations, five maximal Pfaffians of <semantics>5×5</semantics> skew symmetric matrix, and nine <semantics>2×2</semantics> minors of size 3 square matrix. This is a complete classification of such surfaces under certain carefully chosen bounds on the weights of ambient weighted projective spaces and it is largely based on detailed computer-assisted searches by using the computer algebra system MAGMA.