2134/11848755.v1
Alessio Corti
Liana Heuberger
Del Pezzo surfaces with 1/3(1, 1) points
2020
Loughborough University
General Mathematics
Pure Mathematics
2020-02-14 12:14:08
article
https://repository.lboro.ac.uk/articles/Del_Pezzo_surfaces_with_1_3_1_1_points/11848755
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).