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
1. Verfasser: Ran, Ziv
Format: Artikel
Sprache:Englisch
Veröffentlicht: Institute of Mathematics, NAS of Ukraine 2025
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
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author Ran, Ziv
Ran, Ziv
author_facet Ran, Ziv
Ran, Ziv
author_sort Ran, Ziv
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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 $X$.
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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