Resolution of the canonical fiber metrics for a lefschetz fibration
We consider the family of constant curvature fiber metrics for a Lefschetz fibration with regular fibers of genus greater than one. A result of Obitsu and Wolpert is refined by showing that on an appropriate resolution of the total space, constructed by iterated blow-up, this family is log-smooth, i...
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| Format: | Article |
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International Press of Boston, Inc.
2018
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| Online Access: | http://hdl.handle.net/1721.1/116107 https://orcid.org/0000-0002-1494-8228 |
| _version_ | 1811083714654896128 |
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| author | Melrose, Richard B Zhu, Xuwen |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Melrose, Richard B Zhu, Xuwen |
| author_sort | Melrose, Richard B |
| collection | MIT |
| description | We consider the family of constant curvature fiber metrics for a Lefschetz fibration with regular fibers of genus greater than one. A result of Obitsu and Wolpert is refined by showing that on an appropriate resolution of the total space, constructed by iterated blow-up, this family is log-smooth, i.e., polyhomogeneous with integral powers but possible multiplicities, at the preimage of the singular fibers in terms of parameters of size comparable to the logarithm of the length of the shrinking geodesic. |
| first_indexed | 2024-09-23T12:37:57Z |
| format | Article |
| id | mit-1721.1/116107 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T12:37:57Z |
| publishDate | 2018 |
| publisher | International Press of Boston, Inc. |
| record_format | dspace |
| spelling | mit-1721.1/1161072022-10-01T10:10:34Z Resolution of the canonical fiber metrics for a lefschetz fibration Melrose, Richard B Zhu, Xuwen Massachusetts Institute of Technology. Department of Mathematics Melrose, Richard B Zhu, Xuwen We consider the family of constant curvature fiber metrics for a Lefschetz fibration with regular fibers of genus greater than one. A result of Obitsu and Wolpert is refined by showing that on an appropriate resolution of the total space, constructed by iterated blow-up, this family is log-smooth, i.e., polyhomogeneous with integral powers but possible multiplicities, at the preimage of the singular fibers in terms of parameters of size comparable to the logarithm of the length of the shrinking geodesic. 2018-06-05T17:43:10Z 2018-06-05T17:43:10Z 2016-06 2015-07 2018-05-25T17:57:51Z Article http://purl.org/eprint/type/JournalArticle 0022-040X 1945-743X http://hdl.handle.net/1721.1/116107 Melrose, Richard and Xuwen Zhu. "Resolution of the canonical fiber metrics for a Lefschetz fibration." Journal of Differential Geometry, 108 (2018), pp. 295--317. https://orcid.org/0000-0002-1494-8228 https://projecteuclid.org/euclid.jdg/1518490819 Journal of differential geometry Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf International Press of Boston, Inc. arXiv |
| spellingShingle | Melrose, Richard B Zhu, Xuwen Resolution of the canonical fiber metrics for a lefschetz fibration |
| title | Resolution of the canonical fiber metrics for a lefschetz fibration |
| title_full | Resolution of the canonical fiber metrics for a lefschetz fibration |
| title_fullStr | Resolution of the canonical fiber metrics for a lefschetz fibration |
| title_full_unstemmed | Resolution of the canonical fiber metrics for a lefschetz fibration |
| title_short | Resolution of the canonical fiber metrics for a lefschetz fibration |
| title_sort | resolution of the canonical fiber metrics for a lefschetz fibration |
| url | http://hdl.handle.net/1721.1/116107 https://orcid.org/0000-0002-1494-8228 |
| work_keys_str_mv | AT melroserichardb resolutionofthecanonicalfibermetricsforalefschetzfibration AT zhuxuwen resolutionofthecanonicalfibermetricsforalefschetzfibration |