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학술연구/단체지원/교육 등 연구자 활동을 지속하도록 DBpia가 지원하고 있어요.
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We find all $P$-resolutions of quotient surface singularities (especially, tetrahedral, octahedral, and icosahedral singularities) together with their dual graphs, which reproduces (a corrected version of) Jan Steven's list [Manuscripta Math. 1993] of the numbers of $P$-resolutions of each singularities. We then compute the dimensions and Milnor numbers of the corresponding irreducible components of the reduced base spaces of versal deformations of each singularities. Furthermore we realize Milnor fibers as complements of certain divisors (depending only on the singularities) in rational surfaces via the semi-stable minimal model program for 3-folds. Then we compare Milnor fibers with minimal symplectic fillings, where the latter are classified by Bhupal and Ono [Nagoya Math. J. 2012]. As an application, we show that there are 6 pairs of entries in the list of Bhupal and Ono [Nagoya Math. J. 2012] such that two entries in each pairs represent diffeomorphic minimal symplectic fillings.
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참고문헌 (18)
참고문헌 신청
M Artin / 1974 / Algebraic construction of Brieskorn's resolutions / Journal of Algebra 29(2):330~348
Kurt Behnke / 1994 / M-Resolutions and Deformations of Quotient Singularities / American Journal of Mathematics 116(4):881
Mohan Bhupal / 2012 / Symplectic fillings of links of quotient surface singularities / Nagoya Mathematical Journal 207:1~45
M. Bhupal / 2017 / Symplectic fillings of links of quotient surface singularities corrigendum / Nagoya Math. J 225:207~212
Egbert Brieskorn / 1968 / Rationale Singularitaten komplexer Flachen / Inventiones Mathematicae 4(5):336~358
Kurt Behnke / 1994 / M-Resolutions and Deformations of Quotient Singularities / American Journal of Mathematics 116(4):881
Mohan Bhupal / 2012 / Symplectic fillings of links of quotient surface singularities / Nagoya Mathematical Journal 207:1~45
M. Bhupal / 2017 / Symplectic fillings of links of quotient surface singularities corrigendum / Nagoya Math. J 225:207~212
Egbert Brieskorn / 1968 / Rationale Singularitaten komplexer Flachen / Inventiones Mathematicae 4(5):336~358
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