The dualizing sheaf on first-order deformations of toric surface singularities

摘要

We explicitly describe infinitesimal deformations of cyclic quotientsingularities that satisfy one of the deformation conditions introduced byWahl, Kollár–Shepherd-Barron (KSB) and Viehweg. The conclusion is that in manycases these three notions are different from each other. In particular, we see thatwhile the KSB and the Viehweg versions of the moduli space of surfaces ofgeneral type have the same underlying reduced subscheme, theirinfinitesimal structures are different.