Mutations of Laurent Polynomials and Flat Families with Toric Fibers
We give a general criterion for two toric varieties to appear as fibers in a flat family over P¹. We apply this to show that certain birational transformations mapping a Laurent polynomial to another Laurent polynomial correspond to deformations between the associated toric varieties.
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2012 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2012
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148435 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Mutations of Laurent Polynomials and Flat Families with Toric Fibers / N.O. Ilten // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 6 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862709246482710528 |
|---|---|
| author | Ilten, N.O. |
| author_facet | Ilten, N.O. |
| citation_txt | Mutations of Laurent Polynomials and Flat Families with Toric Fibers / N.O. Ilten // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 6 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We give a general criterion for two toric varieties to appear as fibers in a flat family over P¹. We apply this to show that certain birational transformations mapping a Laurent polynomial to another Laurent polynomial correspond to deformations between the associated toric varieties.
|
| first_indexed | 2025-12-07T17:15:55Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148435 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T17:15:55Z |
| publishDate | 2012 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Ilten, N.O. 2019-02-18T12:19:55Z 2019-02-18T12:19:55Z 2012 Mutations of Laurent Polynomials and Flat Families with Toric Fibers / N.O. Ilten // Symmetry, Integrability and Geometry: Methods and Applications. — 2012. — Т. 8. — Бібліогр.: 6 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 14M25; 14D06; 53D37 DOI: http://dx.doi.org/10.3842/SIGMA.2012.047 https://nasplib.isofts.kiev.ua/handle/123456789/148435 We give a general criterion for two toric varieties to appear as fibers in a flat family over P¹. We apply this to show that certain birational transformations mapping a Laurent polynomial to another Laurent polynomial correspond to deformations between the associated toric varieties. This paper is a contribution to the Special Issue “Mirror Symmetry and Related Topics”. The full collection is available at http://www.emis.de/journals/SIGMA/mirror symmetry.html. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Mutations of Laurent Polynomials and Flat Families with Toric Fibers Article published earlier |
| spellingShingle | Mutations of Laurent Polynomials and Flat Families with Toric Fibers Ilten, N.O. |
| title | Mutations of Laurent Polynomials and Flat Families with Toric Fibers |
| title_full | Mutations of Laurent Polynomials and Flat Families with Toric Fibers |
| title_fullStr | Mutations of Laurent Polynomials and Flat Families with Toric Fibers |
| title_full_unstemmed | Mutations of Laurent Polynomials and Flat Families with Toric Fibers |
| title_short | Mutations of Laurent Polynomials and Flat Families with Toric Fibers |
| title_sort | mutations of laurent polynomials and flat families with toric fibers |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148435 |
| work_keys_str_mv | AT iltenno mutationsoflaurentpolynomialsandflatfamilieswithtoricfibers |