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Milnor fibers and symplectic fillings of quotient surface singularities
Park, Heesang,Park, Jongil,Shin, Dongsoo,Urzú,a, Giancarlo Elsevier 2018 Advances in mathematics Vol.329 No.-
<P><B>Abstract</B></P> <P>We determine a one-to-one correspondence between Milnor fibers and minimal symplectic fillings of a quotient surface singularity (up to diffeomorphism type) by giving an explicit algorithm to compare them mainly via techniques from the minimal model program for 3-folds and Pinkham's negative weight smoothing. As by-products, we show that:</P> <P>– Milnor fibers associated to irreducible components of the reduced versal deformation space of a quotient surface singularity are not diffeomorphic to each other with a few obvious exceptions. For this, we classify minimal symplectic fillings of a quotient surface singularity up to diffeomorphism.</P> <P>– Any symplectic filling of a quotient surface singularity is obtained by a sequence of rational blow-downs from a special resolution (so-called the maximal resolution) of the singularity, which is an analogue of the one-to-one correspondence between the irreducible components of the reduced versal deformation space and the so-called <I>P</I>-resolutions of a quotient surface singularity.</P>