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- W2938995569 abstract "Let $V$ be a regular neighborhood of a negative chain of $2$-spheres (i.e. exceptional divisor of a cyclic quotient singularity), and let $B_{p,q}$ be a rational homology ball which is smoothly embedded in $V$. Assume that the embedding is simple, i.e. the corresponding rational blow-up can be obtained by just a sequence of ordinary blow-ups from $V$. Then we show that this simple embedding comes from the semi-stable minimal model program (MMP) for $3$-dimensional complex algebraic varieties under certain mild conditions. That is, one can find all simply embedded $B_{p,q}$'s in $V$ via a finite sequence of antiflips applied to a trivial family over a disk. As applications, simple embeddings are impossible for chains of $2$-spheres with self-intersections equal to $-2$. We also show that there are (infinitely many) pairs of disjoint $B_{p,q}$'s smoothly embedded in regular neighborhoods of (almost all) negative chains of $2$-spheres. Along the way, we describe how MMP gives (infinitely many) pairs of disjoint rational homology balls $B_{p,q}$ embedded in blown-up rational homology balls $B_{n,a} # bar{mathbb{CP}^2}$ (via certain divisorial contractions), and in the Milnor fibers of certain cyclic quotient surface singularities. This generalizes results in [Khodorovskiy-2014], [H. Park-J. Park-D. Shin-2016], [Owens-2017] by means of a uniform point of view." @default.
- W2938995569 created "2019-04-25" @default.
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- W2938995569 date "2021-08-18" @default.
- W2938995569 modified "2023-09-23" @default.
- W2938995569 title "Simple embeddings of rational homology balls and antiflips" @default.
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- W2938995569 doi "https://doi.org/10.2140/agt.2021.21.1857" @default.
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