Del Pezzo orbifold surfaces and toric degenerations

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Edwin Kutas has studied the possible toric degenerations of del Pezzo surface's with orbifold points. He has, with Daniel Cavey (Nottingham PhD student), produced an algorithm to categorise all toric degenerations of del Pezzo surfaces with given singularity content. In addition to this, calculations have been done to prove that various classes of singularity contents cannot occur as a toric degenerations. This problem fits in closely with the EPSRC program grant 3C in G, and leads to natural follow-up questions and further classifications relating to toric degenerations.