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25/07/2012, 14:00 — 15:00 — Room P3.10, Mathematics Building

Yongnam Lee, *Sogang University*

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$Q$-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