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Properties of the moduli set of complete connected projective special real manifolds

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Abstract

We construct a compact convex generating set \(\mathcal {C}_n\) of the moduli set of closed connected projective special real manifolds of fixed dimension n. We show that a closed connected projective special real manifold corresponds to an inner point of \(\mathcal {C}_n\) if and only if it has regular boundary behaviour. Our results can be used to describe deformations of 5d supergravity theories with complete scalar geometries.

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Acknowledgements

This work was partly supported by the German Science Foundation (DFG) under the Research Training Group 1670 and the Collaborative Research Center (SFB) 676. It is based on the main results of Section 5 and technical results of Sections 3 and 4 of my doctoral thesis. Proposition 4.6 is new and not part of my doctoral thesis. I would like to thank my supervisor Vicente Cortés for his continuous support during the writing of my thesis, and I would also like to thank my second examiners Andriy Haydys and Antonio Martínez.

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  1. Department of Mathematics and Center for Mathematical Physics, University of Hamburg, Bundesstraße 55, 20146, Hamburg, Germany

    David Lindemann

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Lindemann, D. Properties of the moduli set of complete connected projective special real manifolds. Math. Z. 303, 37 (2023). https://doi.org/10.1007/s00209-022-03184-4

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