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

  • Context: Graduate 
  • Thread starter Thread starter aaron
  • Start date Start date
Click For Summary
SUMMARY

The discussion centers on identifying examples of Calabi-Yau four-folds with H^(1,1)=1. A specific example provided is the sextic in P^5, which satisfies the condition due to the Lefschetz hyperplane theorem. This theorem confirms that the H^(1,1) value is indeed 1 for this particular case. The conversation highlights the importance of understanding the relationship between Calabi-Yau manifolds and their topological properties.

PREREQUISITES
  • Understanding of Calabi-Yau manifolds
  • Familiarity with Hodge theory
  • Knowledge of the Lefschetz hyperplane theorem
  • Basic concepts of algebraic geometry
NEXT STEPS
  • Research the properties of Calabi-Yau four-folds
  • Study the Lefschetz hyperplane theorem in detail
  • Explore examples of other Calabi-Yau manifolds with different H^(1,1) values
  • Investigate applications of Calabi-Yau manifolds in string theory
USEFUL FOR

Mathematicians, theoretical physicists, and researchers in algebraic geometry interested in the properties and applications of Calabi-Yau manifolds.

aaron
Hi,

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

Aaron
 
Physics news on Phys.org
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.[/color]

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
 

Similar threads

  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 7 ·
Replies
7
Views
4K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 5 ·
Replies
5
Views
3K
  • · Replies 7 ·
Replies
7
Views
5K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 2 ·
Replies
2
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 3 ·
Replies
3
Views
3K