Ajou University repository

GPU Algorithm for Enumerating PL Spheres of Picard Number 4: Application to Toric Topology
Citations

SCOPUS

0

Citation Export

DC Field Value Language
dc.contributor.authorChoi, Suyoung-
dc.contributor.authorJang, Hyeontae-
dc.contributor.authorVallée, Mathieu-
dc.date.issued2024-06-01-
dc.identifier.issn1868-8969-
dc.identifier.urihttps://aurora.ajou.ac.kr/handle/2018.oak/37157-
dc.identifier.urihttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85195469002&origin=inward-
dc.description.abstractThe fundamental theorem for toric geometry states a toric manifold is encoded by a complete non-singular fan, whose combinatorial structure is the one of a PL sphere together with the set of generators of its rays. The wedge operation on a PL sphere increases its dimension without changing its Picard number. The seeds are the PL spheres that are not wedges. A PL sphere is toric colorable if it comes from a complete rational fan. A result of Choi and Park tells us that the set of toric seeds with a fixed Picard number p is finite. In fact, a toric PL sphere needs its facets to be bases of some binary matroids of corank p with neither coloops, nor cocircuits of size 2. We present and use a GPU-friendly and computationally efficient algorithm to enumerate this set of seeds, up to simplicial isomorphism. Explicitly, it allows us to obtain this set of seeds for Picard number 4 which is of main importance in toric topology for the characterization of toric manifolds with small Picard number. This follows the work of Kleinschmidt (1988) and Batyrev (1991) who fully classified toric manifolds with Picard number ≤ 3.-
dc.description.sponsorshipThis work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2019R1A2C2010989).-
dc.language.isoeng-
dc.publisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing-
dc.subject.meshBinary matroids-
dc.subject.meshCharacteristic map-
dc.subject.meshGPU algorithms-
dc.subject.meshGPU-programming-
dc.subject.meshParallel com- puting-
dc.subject.meshPicard number-
dc.subject.meshPL sphere-
dc.subject.meshSimplicial spheres-
dc.subject.meshToric manifold-
dc.subject.meshWeak pseudo-manifold-
dc.titleGPU Algorithm for Enumerating PL Spheres of Picard Number 4: Application to Toric Topology-
dc.typeConference-
dc.citation.conferenceDate2024.6.11. ~ 2024.6.14.-
dc.citation.conferenceName40th International Symposium on Computational Geometry, SoCG 2024-
dc.citation.edition40th International Symposium on Computational Geometry, SoCG 2024-
dc.citation.titleLeibniz International Proceedings in Informatics, LIPIcs-
dc.citation.volume293-
dc.identifier.bibliographicCitationLeibniz International Proceedings in Informatics, LIPIcs, Vol.293-
dc.identifier.doi10.4230/lipics.socg.2024.41-
dc.identifier.scopusid2-s2.0-85195469002-
dc.identifier.urlhttp://drops.dagstuhl.de/opus/institut_lipics.php?fakultaet=04-
dc.subject.keywordbinary matroid-
dc.subject.keywordcharacteristic map-
dc.subject.keywordGPU programming-
dc.subject.keywordparallel computing-
dc.subject.keywordPicard number-
dc.subject.keywordPL sphere-
dc.subject.keywordsimplicial sphere-
dc.subject.keywordtoric manifold-
dc.subject.keywordweak pseudo-manifold-
dc.type.otherConference Paper-
dc.subject.subareaSoftware-
Show simple item record

Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.

Related Researcher

Choi, Suyoung  Image
Choi, Suyoung 최수영
Department of Mathematics
Read More

Total Views & Downloads

File Download

  • There are no files associated with this item.