All fake weighted projective planes and K*-surfaces of Picard number one with integral K^2 are described explicitly by 24 series of degree matrices and by pairs of adjacent such matrices.
Del Pezzo surfaces of Picard number one admitting a torus action
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abstract
We present efficient classification algorithms for log del Pezzo surfaces with torus action of Picard number one and given Gorenstein index. Explicit results are obtained up to Gorenstein index 200.
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K*-surfaces of Picard number one and integral degree
All fake weighted projective planes and K*-surfaces of Picard number one with integral K^2 are described explicitly by 24 series of degree matrices and by pairs of adjacent such matrices.