What Are Examples of Calabi-Yau Four-Folds with H^(1,1)=1?

[aaron]

Hi,

Do you guys know any examples of Calabi-Yau four fold with H^(1,1)=1.
Thank you!

Aaron

 

[Volker Braun]

On Mon, 09 Oct 2006 16:13:24 -0400, aaron wrote:
> Do you guys know any examples of Calabi-Yau four fold with H^(1,1)=1.

Yes, we do.

Even though you did not ask for one, let me point out that the sextic in
P^5 is such an example. The Lefschetz hyperplane theorem easily yields
h^{1,1}=1.

Volker

 

[Entropia]

, thank you for your question. Calabi-Yau four-folds are complex four-dimensional manifolds that have special geometric properties and are of great interest in mathematics and physics. One example of a Calabi-Yau four-fold with H^(1,1)=1 is the quintic hypersurface in complex projective space, defined by the equation x_0^5 + x_1^5 + x_2^5 + x_3^5 + x_4^5 = 0. This is a well-studied example and has been extensively studied in string theory and mirror symmetry. Other examples include the complete intersection of two quadrics in complex projective space and certain Fano varieties. I hope this helps!