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喻yuwei
  • Member for 13 years
  • 中国-云南-昆明
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How do Hodge classes for Calabi-Yau 4-folds compare with the classes for tori?
Explain :the subspace$X^{'}$ of a Weil torus$X$ consists of the Hodge classes,and belongs to$H^{4}\left ( X,\mathbb{Q} \right )$ ,by Hodge decomposition,it contained in $H^{2,2}\left ( X \right )$ ,If it is not Hodge classes,maybe contained in$H^{1,3}\left ( X \right )$ ,$H^{3,1}\left ( X \right )$ ,$H^{0,4}\left ( X \right )$ or$H^{4,0}\left ( X \right )$ .Of course,the Hodge classes of$T$ whether exist in $X$ ,I hope have proof or counterexample .Prove its existence is a very diffficult.
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How do Hodge classes for Calabi-Yau 4-folds compare with the classes for tori?
Carnahan,thank you to fix English grammar fault,About the definition of Weil tori,see Voisin's papers and search in internet.
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de Rham vs Dolbeault Cohomology
5.The cohomology of the projective space ,see akhil mathew's math bolg:[projective space](amathew.wordpress.com/2010/11/22/… )
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What is Mordell-Weil lattice?
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