# Lectures on special Kahler geometry and electric - magnetic duality rotations

@inproceedings{Fr1995LecturesOS,
title={Lectures on special Kahler geometry and electric - magnetic duality rotations},
author={Pietro Giuseppe Fr{\'e}},
year={1995}
}
• P. Fré
• Published 6 December 1995
• Mathematics
68 Citations

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## References

SHOWING 1-10 OF 85 REFERENCES

### Special geometry without special coordinates

• Mathematics
• 1990
Presents a detailed geometric derivation of N=2, 4D supergravity coupled to Abelian vector multiplets (1,1/2,0). The theory is covariant under reparametrisations of the manifold M spanned by the

### A search for non-perturbative dualities of local N = 2 Yang - Mills theories from Calabi - Yau 3-folds

• Mathematics
• 1995
The generalization of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi - Yau 3-fold. Duality

### A search for non-perturbative dualities of local N = 2 Yang - Mills theories from Calabi - Yau 3-folds

• Mathematics
• 1996
The generalization of the rigid special geometry of the vector multiplet quantum moduli space to the case of supergravity is discussed through the notion of a dynamical Calabi - Yau 3-fold. Duality

### A generalization of the momentum mapping construction for quaternionic Kähler manifolds

We present a method of reduction of any quaternionic Kähler manifold with isometries to another quaternionic Kähler manifold in which the isometries are divided out. Our method is a generalization of

### Picard-Fuchs Equations and Special Geometry

• Mathematics
• 1993
We investigate the system of holomorphic differential identities implied by special Kahlerian geometry of four-dimensional N=2 supergravity. For superstring compactifications on Calabi-Yau threefolds