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Polarized Rigid Del Pezzo Surfaces in Low Codimension

Author

Listed:
  • Muhammad Imran Qureshi

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

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.

Suggested Citation

  • Muhammad Imran Qureshi, 2020. "Polarized Rigid Del Pezzo Surfaces in Low Codimension," Mathematics, MDPI, vol. 8(9), pages 1-21, September.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:9:p:1567-:d:412232
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