Quadratic Varieties of Small Codimension
Let ⊂ ℙⁿ⁺ᶜ be a nondegenerate smooth projective variety of dimension defined by quadratic equations. For such varieties, P. Ionescu and F. Russo proved the Hartshorne conjecture on complete intersections, which states that is a complete intersection provided that ≥ 2 + 1. As the extreme case, th...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/213531 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Quadratic Varieties of Small Codimension. Kiwamu Watanabe. SIGMA 21 (2025), 045, 14 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862685350313328640 |
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| author | Watanabe, Kiwamu |
| author_facet | Watanabe, Kiwamu |
| citation_txt | Quadratic Varieties of Small Codimension. Kiwamu Watanabe. SIGMA 21 (2025), 045, 14 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Let ⊂ ℙⁿ⁺ᶜ be a nondegenerate smooth projective variety of dimension defined by quadratic equations. For such varieties, P. Ionescu and F. Russo proved the Hartshorne conjecture on complete intersections, which states that is a complete intersection provided that ≥ 2 + 1. As the extreme case, they also classified with = 2. In this paper, we classify with = 2 − 1.
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| first_indexed | 2026-03-17T11:03:57Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-213531 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T11:03:57Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Watanabe, Kiwamu 2026-02-18T11:26:17Z 2025 Quadratic Varieties of Small Codimension. Kiwamu Watanabe. SIGMA 21 (2025), 045, 14 pages 1815-0659 2020 Mathematics Subject Classification: 14J40; 14J45; 14M10; 14M17; 51N35 arXiv:2405.04002 https://nasplib.isofts.kiev.ua/handle/123456789/213531 https://doi.org/10.3842/SIGMA.2025.045 Let ⊂ ℙⁿ⁺ᶜ be a nondegenerate smooth projective variety of dimension defined by quadratic equations. For such varieties, P. Ionescu and F. Russo proved the Hartshorne conjecture on complete intersections, which states that is a complete intersection provided that ≥ 2 + 1. As the extreme case, they also classified with = 2. In this paper, we classify with = 2 − 1. The author would like to express his sincere gratitude to the anonymous referees for their meticulous reading of his manuscript. Their insightful comments and suggestions have significantly improved various parts of this work. The author knew the proof of Proposition 4.13 in [25] and would like to thank them for teaching how to prove it. Additionally, the author would like to thank Professor Wahei Hara for explaining the parts of the proof that were not understood and for providing a detailed explanation. The author is partially supported by JSPS KAKENHI Grant Numbers 21K03170 and 25K06940. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Quadratic Varieties of Small Codimension Article published earlier |
| spellingShingle | Quadratic Varieties of Small Codimension Watanabe, Kiwamu |
| title | Quadratic Varieties of Small Codimension |
| title_full | Quadratic Varieties of Small Codimension |
| title_fullStr | Quadratic Varieties of Small Codimension |
| title_full_unstemmed | Quadratic Varieties of Small Codimension |
| title_short | Quadratic Varieties of Small Codimension |
| title_sort | quadratic varieties of small codimension |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/213531 |
| work_keys_str_mv | AT watanabekiwamu quadraticvarietiesofsmallcodimension |