Polarized interpolation and normal postulation for curves on Fano hypersurfaces
UDC 514 A general hypersurface $X$ of degree at most $n$ in projective $(n+1)$-space contains curves $C$ of any genus $g\geq 0$ and sufficiently large degree depending on $g$ whose normal and conormal bundles in $X$ have good postulation or natural cohomology in a sense that each twist has either $H...
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2025
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/7878 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512790549102592 |
|---|---|
| author | Ran, Ziv Ran, Ziv |
| author_facet | Ran, Ziv Ran, Ziv |
| author_sort | Ran, Ziv |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-11-01T09:33:57Z |
| description | UDC 514
A general hypersurface $X$ of degree at most $n$ in projective $(n+1)$-space contains curves $C$ of any genus $g\geq 0$ and sufficiently large degree depending on $g$ whose normal and conormal bundles in $X$ have good postulation or natural cohomology in a sense that each twist has either $H^0=0$ or $H^1=0$. This implies a polarized version of the interpolation property for $C$ on $X$. |
| doi_str_mv | 10.3842/umzh.v77i1.7878 |
| first_indexed | 2026-03-24T03:34:23Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-7878 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:34:23Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-78782025-11-01T09:33:57Z Polarized interpolation and normal postulation for curves on Fano hypersurfaces Polarized interpolation and normal postulation for curves on Fano hypersurfaces Ran, Ziv Ran, Ziv Curves on projective hypersurfaces Algebraic Geometry UDC 514 A general hypersurface $X$ of degree at most $n$ in projective $(n+1)$-space contains curves $C$ of any genus $g\geq 0$ and sufficiently large degree depending on $g$ whose normal and conormal bundles in $X$ have good postulation or natural cohomology in a sense that each twist has either $H^0=0$ or $H^1=0$. This implies a polarized version of the interpolation property for $C$ on $X$. УДК 514 Поляризована інтерполяція та нормальне постулювання для кривих на гіперповерхнях Фано Загальна гіперповерхня $X$ степеня не вищого $n$ у проєктивному $(n+1)$-просторі містить криві $C$ довільного роду $g\geq 0$ та достатньо великого степеня, що залежить від $g$, нормальні та конформні жмутки яких у $X$ мають гарну постуляцію або природну когомологію у тому сенсі, що кожне скручування є таким, що $H^0=0$ або $H^1=0$. Це визначає поляризовану версію інтерполяційної властивості для $C$ на $X$. Institute of Mathematics, NAS of Ukraine 2025-10-31 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/7878 10.3842/umzh.v77i1.7878 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 1 (2025); 76 Український математичний журнал; Том 77 № 1 (2025); 76 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/7878/10298 Copyright (c) 2025 ziv ran |
| spellingShingle | Ran, Ziv Ran, Ziv Polarized interpolation and normal postulation for curves on Fano hypersurfaces |
| title | Polarized interpolation and normal postulation for curves on Fano hypersurfaces |
| title_alt | Polarized interpolation and normal postulation for curves on Fano hypersurfaces |
| title_full | Polarized interpolation and normal postulation for curves on Fano hypersurfaces |
| title_fullStr | Polarized interpolation and normal postulation for curves on Fano hypersurfaces |
| title_full_unstemmed | Polarized interpolation and normal postulation for curves on Fano hypersurfaces |
| title_short | Polarized interpolation and normal postulation for curves on Fano hypersurfaces |
| title_sort | polarized interpolation and normal postulation for curves on fano hypersurfaces |
| topic_facet | Curves on projective hypersurfaces Algebraic Geometry |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/7878 |
| work_keys_str_mv | AT ranziv polarizedinterpolationandnormalpostulationforcurvesonfanohypersurfaces AT ranziv polarizedinterpolationandnormalpostulationforcurvesonfanohypersurfaces |