A note on higher obstruction space for surface singularities
Algebraic Geometry
2022-06-03 v2 Symplectic Geometry
Abstract
In this paper we collect some results on the obstruction spaces for rational surface singularities and minimally elliptic surface singularities. Based on the known results we calculate higher obstruction spaces for such surface singularities. The results imply that in general the higher obstruction spaces of deforming semi-log-canonical surfaces do not vanish. We apply the calculation result to show that there is no Li-Tian and Behrend-Fantechi style virtual fundamental class on such moduli space of semi-log-canonical surfaces.
Cite
@article{arxiv.2112.10679,
title = {A note on higher obstruction space for surface singularities},
author = {Yunfeng Jiang},
journal= {arXiv preprint arXiv:2112.10679},
year = {2022}
}
Comments
17 pages, added application to perfect obstruction theory of moduli of slc surfaces, comments are welcome