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Abstract: We pursue the symplectic description of toric Kahler manifolds. There existsa general local classification of metrics on toric Kahler manifolds equippedwith Hamiltonian two-forms due to Apostolov, Calderbank and GauduchonACG. Wederive the symplectic potential for these metrics. Using a method due to Abreu,we relate the symplectic potential to the canonical potential written byGuillemin. This enables us to recover the moment polytope associated withmetrics and we thus obtain global information about the metric. We illustratethese general considerations by focusing on six-dimensional Ricci flat metricsand obtain Ricci flat metrics associated with real cones over L^{pqr} andY^{pq} manifolds. The metrics associated with cones over Y^{pq} manifolds turnout to be partially resolved with two blowup parameters taking specialnon-zerovalues. For a fixed Y^{pq} manifold, we find explicit metrics forseveral inequivalent blow-ups parametrised by a natural number k in the range0


Autor: Aswin K. Balasubramanian IITM, Suresh Govindarajan IITM, Chethan N. Gowdigere ICTP

Fuente: https://arxiv.org/







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