查看“︁小平消沒定理”︁的源代码

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小平消沒定理是[[複幾何]]及[[代數幾何]]中的重要結果，在[[複流形的分類]]問題(例如Enriques-Kodaira Classification)上扮演着重要角色。


== 經典命題 ==
[[小平邦彦]]起初使用流形上的[[霍奇理論]]証明，當q>0

:::<math> H^q(M, K_M\otimes L) \cong H^q(M,\Omega^n(L))= 0 </math>,

以上''M'' 為任何緊致[[凱勒流形]]，<math>K_M</math>是''M''上的[[正規線叢]]，<math>L \rightarrow M</math>是[[正線叢]]。這個命題之後被推廣為小平 中野消沒定理：

::: <math>H^q(M,\Omega^p(L)) = 0 </math>

當<math>p+q>n</math>。<math>\Omega^p(L)</math>代表在''L''上的所有[[全純]] (p,0)-形式組成的[[層]]。
== 應用及推廣 ==

[[小平嵌入定理]]

[[複流形分類]]

Kawamata-Viehweg Vanishing theorem

== 參考 ==
* {{Citation
  | last = Deligne
  | first = Pierre
  | last2 = Illusie
  | first2 = Luc
  | title = Relèvements modulo p<sup>2</sup> et décomposition du complexe de de Rham
  | journal = Inventiones Mathematicae
  | volume = 89
  | pages = 247–270
  | year = 1987
  | doi = 10.1007/BF01389078 }}
*{{Citation | last1=Esnault | first1=Hélène | last2=Viehweg | first2=Eckart | title=Lectures on vanishing theorems | publisher=Birkhäuser Verlag | series=DMV Seminar | isbn=978-3-7643-2822-1 | id={{MathSciNet | id = 1193913}} | year=1992 | volume=20}}
*[[菲利普·A·格里菲瑟茨|Phillip Griffiths]] and {{tsl|en|Joe Harris (mathematician)||Joseph Harris}}, ''Principles of Algebraic Geometry''
*{{Citation | last1=Raynaud | first1=Michel | author1-link=Michel Raynaud | title=C. P. Ramanujam---a tribute | publisher=[[施普林格科学+商业媒体|Springer-Verlag]] | location=Berlin, New York | series=Tata Inst. Fund. Res. Studies in Math. | id={{MathSciNet | id = 541027}} | year=1978 | volume=8 | chapter=Contre-exemple au vanishing theorem en caractéristique p>0 | pages=273–278}}
*{{cite book
  | last = Viehweg
  | first = Eckart
  | authorlink = Eckart Viehweg
  | last2 = Esnault
  | first2 = Hélène
  | authorlink2 = Hélène Esnault
  | title = Lectures on Vanishing Theorems
  | publisher = {{tsl|en|Birkhäuser||Birkhäuser}}
  | date = 1992
  | location = 
  | pages = 
  | url = http://www.uni-due.de/%7Emat903/books/esvibuch.pdf
  | doi = 
  | id = 
  | isbn = 3-7643-2822-3
  | access-date = 2009-07-18
  | archive-date = 2021-01-05
  | archive-url = https://web.archive.org/web/20210105181026/https://www.uni-due.de/~mat903/books/esvibuch.pdf
  | dead-url = no
  }}

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[[Category:代数几何定理]]