16
votes
4answers
1k views

Example of a smooth morphism where you can't lift a map from a nilpotent thickening?

Definition. A locally finitely presented morphism of schemes $f\colon X\to Y$ is smooth (resp. unramified, resp. ├ętale) if for any affine scheme $T$, any closed subscheme $T_0$ defined by a square ...
5
votes
1answer
444 views

obstruction to smooth lifting of smooth schemes

According to general theory, for a square zero thickening defined by an ideal I: SpecA -> SpecA', there is an obstruction of lifting a smooth scheme X over A to a smooth scheme over A' living in ...
6
votes
0answers
557 views

“a theory of generalized Donaldson-Thomas invariants” by Joyce & Song

Is anyone else working through this paper : http://arxiv.org/abs/0810.5645 ? I am trying to verifying example 6.2 (m=2 for simplicity) using only the definitions, namely: J^{2\alpha}(\tau) = -1/4 ...