Polarized Rigid Del Pezzo Surfaces in Low Codimension

Muhammad Imran Qureshi
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Muhammad Imran Qureshi: Department of Mathematics, King Fahd University of Petroleum & Minerals (KFUPM), Dhahran 31261, Saudi Arabia

Mathematics, 2020, vol. 8, issue 9, 1-21

Abstract: We provide explicit graded constructions of orbifold del Pezzo surfaces with rigid orbifold points of type k i × 1 r i ( 1 , a i ) : 3 ≤ r i ≤ 10 , k i ∈ Z ≥ 0 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 5 × 5 skew symmetric matrix, and nine 2 × 2 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.

Keywords: orbifold del pezzo surfaces; hypersurfaces; complete intersections; pfaffians; graded ring constructions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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