Box graphs and resolutions I
Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Elsevier
2016-04-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0550321316000377 |
| _version_ | 1811239069767696384 |
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| author | Andreas P. Braun Sakura Schäfer-Nameki |
| author_facet | Andreas P. Braun Sakura Schäfer-Nameki |
| author_sort | Andreas P. Braun |
| collection | DOAJ |
| description | Box graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial) toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5) by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs. |
| first_indexed | 2024-04-12T12:53:24Z |
| format | Article |
| id | doaj.art-1bf52def00634034a73f370b117eb718 |
| institution | Directory Open Access Journal |
| issn | 0550-3213 1873-1562 |
| language | English |
| last_indexed | 2024-04-12T12:53:24Z |
| publishDate | 2016-04-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-1bf52def00634034a73f370b117eb7182022-12-22T03:32:23ZengElsevierNuclear Physics B0550-32131873-15622016-04-01905C44747910.1016/j.nuclphysb.2016.02.002Box graphs and resolutions IAndreas P. Braun0Sakura Schäfer-Nameki1University of Oxford, Mathematical Institute, Andrew Wiles Building, Woodstock Rd., Oxford OX2 6GG, UKDepartment of Mathematics, King's College, The Strand, London WC2R 2LS, UKBox graphs succinctly and comprehensively characterize singular fibers of elliptic fibrations in codimension two and three, as well as flop transitions connecting these, in terms of representation theoretic data. We develop a framework that provides a systematic map between a box graph and a crepant algebraic resolution of the singular elliptic fibration, thus allowing an explicit construction of the fibers from a singular Weierstrass or Tate model. The key tool is what we call a fiber face diagram, which shows the relevant information of a (partial) toric triangulation and allows the inclusion of more general algebraic blowups. We shown that each such diagram defines a sequence of weighted algebraic blowups, thus providing a realization of the fiber defined by the box graph in terms of an explicit resolution. We show this correspondence explicitly for the case of SU(5) by providing a map between box graphs and fiber faces, and thereby a sequence of algebraic resolutions of the Tate model, which realizes each of the box graphs.http://www.sciencedirect.com/science/article/pii/S0550321316000377 |
| spellingShingle | Andreas P. Braun Sakura Schäfer-Nameki Box graphs and resolutions I Nuclear Physics B |
| title | Box graphs and resolutions I |
| title_full | Box graphs and resolutions I |
| title_fullStr | Box graphs and resolutions I |
| title_full_unstemmed | Box graphs and resolutions I |
| title_short | Box graphs and resolutions I |
| title_sort | box graphs and resolutions i |
| url | http://www.sciencedirect.com/science/article/pii/S0550321316000377 |
| work_keys_str_mv | AT andreaspbraun boxgraphsandresolutionsi AT sakuraschafernameki boxgraphsandresolutionsi |