ترغب بنشر مسار تعليمي؟ اضغط هنا

A remark on the Hard Lefschetz Theorem for Kahler orbifolds

165   0   0.0 ( 0 )
 نشر من قبل Dan Zaffran
 تاريخ النشر 2009
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We give a proof of the hard Lefschetz theorem for orbifolds that does not involve intersection homology. This answers a question of Fulton. We use a foliated version of the hard Lefschetz theorem due to El Kacimi.



قيم البحث

اقرأ أيضاً

101 - John P. DAngelo 2017
We prove that a certain positivity condition, considerably more general than pseudoconvexity, enables one to conclude that the regular order of contact and singular order of contact agree when these numbers are $4$.
81 - Igor Nikolaev 2020
We prove Faltings Finiteness Theorem using Rieffels classification of the noncommutative tori.
In the present paper, we show that given a compact Kahler manifold $(X,omega)$ with a Kahler metric $omega$, and a complex submanifold $Vsubset X$ of positive dimension, if $V$ has a holomorphic retraction structure in $X$, then any quasi-plurisubhar monic function $varphi$ on $V$ such that $omega|_V+sqrt{-1}partialbarpartialvarphigeq varepsilonomega|_V$ with $varepsilon>0$ can be extended to a quasi-plurisubharmonic function $Phi$ on $X$, such that $omega+sqrt{-1}partialbarpartial Phigeq varepsilonomega$ for some $varepsilon>0$. This is an improvement of results in cite{WZ20}. Examples satisfying the assumption that there exists a holomorphic retraction structure contain product manifolds, thus contains many compact Kahler manifolds which are not necessarily projective.
83 - Qian Guan 2018
In this note, we answer a question on the extension of $L^{2}$ holomorphic functions posed by Ohsawa.
Let $(X,omega)$ be a compact K{a}hler manifold with a K{a}hler form $omega$ of complex dimension $n$, and $Vsubset X$ is a compact complex submanifold of positive dimension $k<n$. Suppose that $V$ can be embedded in $X$ as a zero section of a holomor phic vector bundle or rank $n-k$ over $V$. Let $varphi$ be a strictly $omega|_V$-psh function on $V$. In this paper, we prove that there is a strictly $omega$-psh function $Phi$ on $X$, such that $Phi|_V=varphi$. This result gives a partial answer to an open problem raised by Collins-Tosatti and Dinew-Guedj-Zeriahi, for the case of K{a}hler currents. We also discuss possible extensions of Kahler currents in a big class.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا