K-stable del Pezzo surfaces with a single quotient singularity of type 1/(mn-1)(1,n) and two exceptional curves in the minimal resolution are exactly S^4_{2,2}, S^5_{2,2}, S^5_{3,2}, S^6_{3,2}, S^6_{4,2}, S^7_{4,2}, S^5_{3,3}, S^6_{4,3}; S^3_{2,2} and S^7_{5,2} are strictly semistable.
$\delta$-invariants of Du Val del Pezzo surfaces of degree 2
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In this article, we compute $\delta$-invariants of Du Val del Pezzo surfaces of degree 2.
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K-stability of del Pezzo surfaces with a single quotient singularity
K-stable del Pezzo surfaces with a single quotient singularity of type 1/(mn-1)(1,n) and two exceptional curves in the minimal resolution are exactly S^4_{2,2}, S^5_{2,2}, S^5_{3,2}, S^6_{3,2}, S^6_{4,2}, S^7_{4,2}, S^5_{3,3}, S^6_{4,3}; S^3_{2,2} and S^7_{5,2} are strictly semistable.