We explicitly describe infinitesimal deformations of cyclic quotient singularities that satisfy one of the deformation conditions introduced by Wahl, Kollár-ShepherdBarron (KSB) and Viehweg. The conclusion is that in many cases these three notions are different from each other. In particular, we see that while the KSB and the Viehweg versions of the moduli space of surfaces of general type have the same underlying reduced subscheme, their infinitesimal structures are different.
All Science Journal Classification (ASJC) codes
- Applied Mathematics