posted on 2020-02-14, 12:14authored byAlessio Corti, Liana Heuberger
We classify non-smooth del Pezzo surfaces with 1/3(1, 1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake in Classification of log del Pezzo surfaces of index three, arXiv:1401.1283 [math.AG]), we tabulate their biregular invariants, we give good model constructions for surfaces in all families as degeneracy loci in rep quotient varieties, and we prove that precisely 26 families admit qG-degenerations to toric surfaces. This work is part of a program to study mirror symmetry for orbifold del Pezzo surfaces (Akhtar et al. in Proc Am Math Soc 144(2):513–527, 2016).
This is a post-peer-review, pre-copyedit version of an article published in Manuscripta Mathematica. The final authenticated version is available online at: https://doi.org/10.1007/s00229-016-0870-y.