Systematic orbifold constructions of Schellekens' vertex operator algebras from Niemeier lattices

We present a systematic, rigorous construction of all 70 strongly rational, holomorphic vertex operator algebras $V$ central charge 24 with non-zero weight-one space $V_1$ as cyclic orbifold constructions associated the Niemeier lattice $V_N$ and certain 226 short automorphisms in $\operatorname{Aut}(V_N)$. show that up to algebraic conjugacy these are exactly generalised deep holes, introduced arXiv:1910.04947, additional property their orders equal those corresponding outer automorphisms. Together arXiv:1708.05990 arXiv:1910.04947 this gives three different uniform algebras, which related through 11 classes $\operatorname{Co}_0$. Finally, by considering inverse automorphisms, we give first systematic proof result each algebra is uniquely determined Lie structure $V_1$.