Simple embeddings of rational homology balls and antiflips

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dc.contributor.authorPark, Heesang
dc.contributor.authorShin, Dongsoo
dc.contributor.authorUrzua, Giancarlo
dc.date.accessioned2024-01-10T12:37:01Z
dc.date.available2024-01-10T12:37:01Z
dc.date.issued2021
dc.description.abstractLet V be a regular neighborhood of a negative chain of 2-spheres (ie an exceptional divisor of a cyclic quotient singularity), and let B-p,B-q be a rational homology ball which is smoothly embedded in V. Assume that the embedding is simple, ie the corresponding rational blowup can be obtained by just a sequence of ordinary blowups from V. Then we show that this simple embedding comes from the semistable minimal model program (MMP) for 3-dimensional complex algebraic varieties under certain mild conditions. That is, one can find all simply embedded B-p,B-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. We also show that there are (infinitely many) pairs of disjoint Bp;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 Bp;q embedded in blown-up rational homology balls B-n,B-a (sic) CP2 (via certain divisorial contractions), and in the Milnor fibers of certain cyclic quotient surface singularities. This generalizes results of Khodorovskiy (2012, 2014), H Park, J Park and D Shin (2016) and Owens (2018) by means of a uniform point of view.
dc.format.extent24 páginas
dc.fuente.origenWOS
dc.identifier.doi10.2140/agt.2021.21.1857
dc.identifier.issn1472-2739
dc.identifier.urihttps://doi.org/10.2140/agt.2021.21.1857
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/76726
dc.identifier.wosidWOS:000688060400008
dc.information.autorucFacultad de Matemáticas; Urzua Elia, Giancarlo Andres; S/I; 13222
dc.issue.numero4
dc.language.isoen
dc.nota.accesoSin adjunto
dc.pagina.final1880
dc.pagina.inicio1857
dc.publisherGEOMETRY & TOPOLOGY PUBLICATIONS
dc.revistaALGEBRAIC AND GEOMETRIC TOPOLOGY
dc.rightsregistro bibliográfico
dc.subjectSMOOTHINGS
dc.subjectSURFACES
dc.titleSimple embeddings of rational homology balls and antiflips
dc.typeartículo
dc.volumen21
sipa.codpersvinculados13222
sipa.indexWOS
sipa.trazabilidadCarga SIPA;09-01-2024
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