Log-terminal smoothings of graded normal surface singularities

Details Log-terminal smoothings of graded normal surface singularities Log-terminal smoothings of graded normal surface singularities

2011-10-13

arxiv.org/abs/1110.2979v2

Mathematics

Algebraic Geometry

16 pages, Latex; typos removed, Theorem 4.3 now correctly attributed to K. Watanabe

Scientific paper

Recent work ([14], [1]) has produced a complete list of weighted homogeneous surface singularities admitting smoothings whose Milnor fibre has only trivial rational homology (a "rational homology disk"). Though these special singularities form an unfamiliar class and are rarely even log-canonical, we prove the Theorem. A rational homology disk smoothing of a weighted homogeneous surface singularity can always be chosen so that the total space is log-terminal. In particular, this smoothing is $\Q$-Gorenstein. The key idea is to define a finite "graded discrepancy" of a normal graded domain with $\Q$-Cartier canonical divisor, and to study its behavior for a smoothing.

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