It is known that Godeaux’s construction of surfaces with χ = 1, K2 = 1 as the quotient of a quintic surface by an action of the cyclic group of order 5 can be modified to work in chacteristic 5, with any of the possible group schemes of order 5. These cases can all be put together into a single deformation family in mixed characteristic, and a similar construction also produces non-singular Calabi-Yau 3-folds with polarisation of degree A3 = 1 and Pic0 containing any of the group schemes ℤ/5 or μ5 or α5. For more information, see this website.
The aim of the talk is to do the same for Godeaux surfaces and CY 3-folds with 3-torsion.
This video was produced by the Japan-US Mathematics Institute and forms part of JAMI Conference 2022.
