Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space
We prove a version of the BKK theorem for the ring of conditions of a spherical homogeneous space G/H. We also introduce the notion of a ring of complete intersections, firstly for a spherical homogeneous space and secondly for an arbitrary variety. Similarly to the ring of conditions of the torus,...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2020 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2020
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210594 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space. Kiumars Kaveh and Askold G. Khovanskii. SIGMA 16 (2020), 016, 12 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862547209056157696 |
|---|---|
| author | Kaveh, Kiumars Khovanskii, Askold G. |
| author_facet | Kaveh, Kiumars Khovanskii, Askold G. |
| citation_txt | Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space. Kiumars Kaveh and Askold G. Khovanskii. SIGMA 16 (2020), 016, 12 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We prove a version of the BKK theorem for the ring of conditions of a spherical homogeneous space G/H. We also introduce the notion of a ring of complete intersections, firstly for a spherical homogeneous space and secondly for an arbitrary variety. Similarly to the ring of conditions of the torus, the ring of complete intersections of G/H admits a description in terms of volumes of polytopes.
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| first_indexed | 2025-12-17T12:03:35Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210594 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-17T12:03:35Z |
| publishDate | 2020 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kaveh, Kiumars Khovanskii, Askold G. 2025-12-12T10:35:12Z 2020 Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space. Kiumars Kaveh and Askold G. Khovanskii. SIGMA 16 (2020), 016, 12 pages 1815-0659 2020 Mathematics Subject Classification: 14M27; 14M25; 14M10 arXiv:1911.00118 https://nasplib.isofts.kiev.ua/handle/123456789/210594 https://doi.org/10.3842/SIGMA.2020.016 We prove a version of the BKK theorem for the ring of conditions of a spherical homogeneous space G/H. We also introduce the notion of a ring of complete intersections, firstly for a spherical homogeneous space and secondly for an arbitrary variety. Similarly to the ring of conditions of the torus, the ring of complete intersections of G/H admits a description in terms of volumes of polytopes. We are grateful to the anonymous referee for careful reading of the paper and several invaluable suggestions and corrections. The first author is partially supported by a National Science Foundation grant (grant ID: 1601303). The second author is partially supported by the Canadian grant No. 156833-12. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space Article published earlier |
| spellingShingle | Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space Kaveh, Kiumars Khovanskii, Askold G. |
| title | Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space |
| title_full | Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space |
| title_fullStr | Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space |
| title_full_unstemmed | Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space |
| title_short | Intersections of Hypersurfaces and Ring of Conditions of a Spherical Homogeneous Space |
| title_sort | intersections of hypersurfaces and ring of conditions of a spherical homogeneous space |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210594 |
| work_keys_str_mv | AT kavehkiumars intersectionsofhypersurfacesandringofconditionsofasphericalhomogeneousspace AT khovanskiiaskoldg intersectionsofhypersurfacesandringofconditionsofasphericalhomogeneousspace |