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
Datum:2025
1. Verfasser: Watanabe, Kiwamu
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2025
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
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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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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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