Title    name KIAS Seminar     Title Flipping surfaces   Speaker Giancarlo Urzua   Date 2012-07-02   Host   Place KIAS   File     Abstract : Let $X$ be a projective surface with only $T$-singularities. Assume it has a $mathbb{Q}$-Gorenstein smoothing $X subset mathcal{X} to 0 in mathbb{D}$ over a smooth curve germ, whose smooth fibers are of general type. What is the Koll'ar--Shepherd-Barron stable family of $mathcal{X} to mathbb{D}$? In this talk we will show how to find explicitly its minimal model. The main point is to relate Mori flips of type $k1A$ and $k2A$ via deformations and continued fractions. We will discuss certain properties such as the existence of a universal family for them, and the amount of these families over a fixed cyclic quotient singularity (this allows fast calculations). This is a joint work with P. Hacking and J. Tevelev.

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