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DTSTART:20210101T000000
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DTSTART;TZID=Asia/Seoul:20220329T153000
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SUMMARY:Dongsoo Shin\, Deformations of Sandwiched Surface Singularities and the Semistable Minimal Model Program
DESCRIPTION:     Speaker\n\n\nDongsoo Shin\nChungnam National Univ.\n\n\n\n\n\nA sandwiched surface singularity is a rational surface singularity that admits a birational map to the complex projective plane. de Jong and van Straten [Duke Math J 1998] prove that deformations of sandwiched surface singularities are induced from special deformations of germs of plane curve singularities (called picture deformations). On the other hand\, Kollár and Shepherd-Barron [Invent Math 1988] conjecture that deformations of any rational surface singularities are described by special partial modifications (called P-modifications). So there are two different descriptions of deformations of sandwiched surface singularities. We provide a way to find a correspondence between picture deformations and P-resolutions (roughly speaking\, normal P-modifications with mild singularities) using the semistable minimal model program for complex 3-folds. As applications\, 1. we provide correspondence between various deformation theories of cyclic quotient surface singularities 2. We give proofs of Kollár conjecture for certain weighted homogeneous surface singularities.
URL:https://ccg.ibs.re.kr/event/2022-03-29-1530/
LOCATION:B266\, IBS\, Korea\, Republic of
CATEGORIES:Algebraic Geometry Seminar
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