Summer Lectures in Geometry

$Q$-Gorenstein deformation theory and its applications

The 2nd lecture will explain several methods for constructions of surfaces of general type via $Q$-Gorenstein smoothings. After the paper by Lee and Park, which constructs a simply connected Campedelli surface, several interesting examples of surfaces of general type with ${p}_{g}=0$ were constructed via $Q$-Gorenstein smoothings. Now, these $Q$-Gorenstein smoothing methods are extended to some other type of surfaces and to surfaces in positive characteristics.

References

• J. Kollár and N. I. Shepherd-Barron, Threefolds and deformations of surface singularities, Invent. Math. 91 (1988), 299-338.
• Y. Lee and J. Park, A simply connected surface of general type with ${p}_{g}=0$ and ${K}^{2}=2$, Invent. Math. 170 (2007), 483-505.
• Y. Lee and N. Nakayama, Simply connected surfaces of general type in positive characteristic via deformation theory, preprint 2011 (arXiv:1103.5185, to appear in PLMS).
Session 2

For detailed overviews of each course see http://camgsd.ist.utl.pt/encontros/slg/.