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arXiv · 2205.11165

Deformations of sandwiched surface singularities and the minimal model program

Heesang Park·Dongsoo Shin
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Abstract

We investigate the correspondence between three theories of deformations of rational surface singularities: de Jong and van Straten's picture deformations, Kollár's P-resolutions, and Pinkham's smoothings of negative weights. We provide an explicit method for obtaining, from a given deformation in one theory, deformations in other theories that parameterize the same irreducible components of the deformation space of the singularity. We employ the semi-stable minimal model program significantly for this purpose. We prove Kollár conjecture for various sandwiched surface singularities as an application.

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Heesang Park, Dongsoo Shin. 2022-12-15. Deformations of sandwiched surface singularities and the minimal model program. https://arxiv.org/abs/2205.11165

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