Del Pezzo surfaces with a single 1/k(1,1) singularity

On deformations of toric Fano varieties

“…In many cases this produces smoothings of X P . For instance, Cavey and Prince [23] have successfully applied the scaffolding method to construct deformations of toric del Pezzo surfaces to del Pezzo surfaces with a single 1 k (1, 1) singularity.…”

Biregular models of log Del Pezzo surfaces with rigid singularities

“…Such surfaces with m × 1 3 (1, 1) points have been classified by Corti and Heuberger in [CH17]. The classification with a single orbifold point of type 1 r (1, 1) is provided by Cavey and Prince [CP17]. The log Del Pezzo surfaces have also been studied from the point of view of the existence of orbifold Kahler-Einstein metric on such surfaces in [CS13,CPS10,KP15] starting with [JK01].…”

“…The first model in the above table has already been discussed in [CP17] where its description as a toric variety has been provided.…”

“…The first model has been discussed in [CP17] and its toric description has also been provided by embedding it in a singular toric variety. In the case of Fano index 2 we get two biregular models which are indexed by 2 parameters giving rise to an infinite series of one parameter biregular models in each case.…”

“…It is called an R-singularity it it is is rigid under any Q-Gorenstein smoothing. We use the following characterization of a cyclic quotient singularity to be a T -singularity and R-singularity, appeared in [CP17].…”